The BJP had fielded 36 candidates and also supported independent candidates in remaining four seats. If the party misses majority, it may form an alliance with Maharashtrawadi Gomantak Party (MGP).
Defence Minister Manohar Parrikar led the party's campaign in Goa. BJP chief Amit Shah had earlier hinted that the new government could work under the leadership of Mr Parrikar, fueling speculation of his return to state politics.
Mr Parrikar, who became the Chief Minister of Goa in 2012, was later elevated to Prime Minister Narendra Modi's cabinet in 2014. Laxmikant Parsekar succeeded as the state's Chief Minister.
According to the exit polls, Arvind Kejriwal's Aam Aadmi Party (AAP), which is making a debut in the state, is expected to win just three seats in the assembly elections. It also predicted a big win for BJP in Uttar Pradesh and Uttarakhand. However, please remember, exit polls predictions are known for going wide off the mark.
The counting for all the five states - Uttar Pradesh, Punjab, Goa, Uttarakhand and Manipur - will begin at 7 am.