The bypoll was necessitated following the resignation of the former Goa Chief Minister Parrikar.
Parrikar cast his vote at a booth in the heart of the city.
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The constituency has 22,057 voters, of whom majority are women (11,335).
The voting is taking place across 30 booths. There is no sensitive or hyper-sensitive booth in the constituency.
BJP's Siddharth Kuncolienkar, Congress's Surendra Furtado and two independents - Samir Kelekar and Sadanand Vaigankar - are in the fray for the bypoll.
Joint Chief Electoral Officer Narayan Navti today appealed to the people to come out in large numbers to vote.
A company of Central Industrial Security Force (CISF) has arrived in Goa for patrolling along with the state police.
During the 2012 state Legislative Assembly election, the constituency had witnessed 77.13% voting, giving a winning edge to Parrikar.
The counting of votes will be held on March 16 at Entertainment Society of Goa (ESG) compound near here.