The Senate voted 34-1 to approve the measure on Wednesday.
Under the Kentucky proposal, Bible courses would be offered as electives, meaning students could decide whether to take them.
Republican Sen. Joe Bowen of Owensboro, the bill's sponsor, said the intention is to acquaint students with a book that has had tremendous impact on American society and western culture.
Democratic Sen. Kathy Stein of Lexington said the measure is unnecessary because nothing currently prohibits Kentucky public schools from teaching about the Bible.
A similar measure overwhelmingly passed in the Senate last year only to die in the House.
The legislation is Senate Bill 56.