Voting opened at 07:00 local time on Sunday (22:00 GMT Saturday).
Mr Abe called the election amid rebounding approval ratings after a record low over the summer and with the opposition largely in disarray.
If, as predicted, Mr Abe is re-elected, he will be on track to become Japan's longest serving post-war leader.
An early challenge from the popular governor of Tokyo, Yuriko Koike, appears to be fizzling out, according to the BBC's Tokyo correspondent Rupert Wingfield-Hayes.
One observer described voting for Mr Abe's Liberal Democratic Party as TINA - there is no alternative.
Mr Abe is hoping his party will win a two-thirds majority, allowing him to make constitutional changes. In particular, he wants to change Japan's self-defence force into a national army for the first time since the Second World War.
Mr Abe announced the election on 25 September, saying he needed a fresh mandate in order to deal with the "national crises" facing Japan.
The crises include North Korea, which has threatened to "sink" Japan into the sea. Pyongyang has also fired two missiles over Hokkaido, an island to the north.
Other areas up for debate in the election are the post-Fukushima nuclear policy and the issue of tax.
The polls close at 20:00 local time.
Photo copyright: EPA (Caption: Millions of Japanese are voting on Sunday)