Polling picked up pace in the afternoon as voters turned out in large numbers in the total 1476 booths in six assembly segments - Goriakothi, Maharajganj, Ekma, Manjhi,Baniapur and Taraiya seat spread over Saran and Siwan districts, election office sources said.
There was no report of any untoward incident from anywhere in the constituency, the sources said.
Elaborate security arrangements were made and 20 companies of central para military forces, 10 companies of Bihar Military Police and 7000 additional policemen have been deployed to ensure free and fair polls, they said.
The by-poll was necessitated by the death of the sitting RJD MP Uma Shankar Singh earlier this year.
A total six candidates, including JD(U) nominee and state Education Minister Prashant Kumar Shahi, RJD's Prabhunath Singh and Congress' Jitendra Swami, are in fray.
All the three contending parties are keenly watching the outcome of Maharajganj parliamentary poll as it would reflect the public mood and set the tone for the 2014 general elections.