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.