Polls opened at 7 a.m. (2200 GMT) and will close at 8 p.m. (1100 GMT), when major TV broadcasters will issue exit polls forecasting results.
An LDP win would usher in a government committed to a tough stance in a territorial row with China, a pro-nuclear energy policy despite last year's Fukushima disaster and a potentially risky prescription for hyper-easy monetary policy and big fiscal spending to beat deflation and tame a strong yen.
Media surveys have forecast the LDP will win a big majority in parliament's powerful 480-seat lower house, just three years after a devastating defeat that ended more than 50 years of almost non-stop rule by the business-friendly party.
Together with a small ally, Abe's LDP could even gain the two-thirds majority needed to break through a policy deadlock that has plagued successive governments for years.
Voters expressed disappointment with Prime Minister Yoshihiko Noda's Democratic Party of Japan (DPJ), which surged to power in 2009 promising to pay more heed to consumers than companies.
Many voters now feel the DPJ failed to meet its election pledges as it struggled to govern and cope with last year's huge earthquake, tsunami and nuclear disaster, and then pushed through an unpopular sales tax increase with LDP help.
"Nothing has changed for the better," said Masaki Kondo, a 29-year old worker at a securities firm, who voted DPJ three years ago but said he was switching his support to Abe's party
The DPJ has been hit by defections and is likely to win fewer than 100 seats, less than a third of its tally in 2009.
But some voters also doubted whether a return to LDP rule was a true antidote to the many challenges that face Japan from regional tensions to economic malaise.
"The Democrats are out because they have been unable to implement their policy manifesto and are divided internally. But that doesn't mean I support the LDP," said Yosuke Matsumoto, 33, who owns a marketing firm. "Nothing will change under them."
Voter distaste for both major parties has spawned a clutch of new parties including the right-leaning Japan Restoration Party founded by popular Osaka Mayor Toru Hashimoto.
Hashimoto's supporters in Osaka said the country needed strong leadership at a time when it sees its dominance in the region challenged by China and South Korea.
"What we need is a shake-up," said 77-year old Nobuo Sano.
LDP leader Abe, 58, who quit as premier in 2007 after a year in office, has been talking tough in a row with China over uninhabited isles in the East China Sea, although some experts say he may temper his hard line with pragmatism once in office.
The soft-spoken grandson of a prime minister, who would become Japan's seventh premier in six years, Abe also wants to loosen the limits of a 1947 pacifist constitution on the military, so Japan can play a bigger global security role.
China's official Xinhua news agency said in an editorial Japan's winning party should formulate its foreign policy with a long-term perspective to repair ties with neighbours.
The news agency said it was a "troubling sign" that some parties in the election had promised to take a tough stand on territorial disputes and increase military spending.
The LDP, which promoted atomic energy during its decades-long reign, is expected to be friendly to nuclear utilities, although deep public safety concerns remain a barrier to business-as-usual for the industry.
A mother of two voting in Tokyo said she could not support the LDP because of its stand on nuclear energy. "I have children and I have to think about their future," said the 43-year old woman who declined to give her name.
She said she was voting for the Tomorrow Party of Japan, which aims to shut nuclear reactors in 10 years, much earlier than the current government's goal of the 2030s.
High on the list of voter concerns is the economy, which is in its fourth recession since 2000 amid slowing global growth, a strong yen and the territorial row with China.
"A strong economic policy is what I expect from the LDP," said 40-year old Tetsuo Ueda, who runs a bar in Tokyo. He said his business has suffered in the past three years.
Abe has called for "unlimited" monetary easing and big spending on public works to rescue the economy. But such policies, a centrepiece of the LDP's platform for decades, have been criticised by many as wasteful pork-barrel politics.
Many economists say that prescription for "Abenomics" could create temporary growth and enable the government to go ahead with a planned initial sales tax rise in 2014 to help curb a public debt now twice the size of gross domestic product.
But it looks unlikely to cure deeper ills or bring sustainable growth, and risks triggering a market backlash if investors decide Japan has lost control of its finances.
Japan's economy has been stuck in the doldrums for decades, its population ageing fast and big corporate brands faltering, making "Japan Inc" a synonym for decline.
Consumer electronics firms such as Sony Corp are struggling with competition from foreign rivals and burdened by a strong yen, which makes their products cost more overseas.
"I'm really worried about the economy. I hope the LDP will work on that first," said Masao Ibuki, a 90-year old pensioner who voted for the LDP in Tokyo.