If the measure passes the Senate and wins the constitutionally required voter approval, the change would take effect in 2019, the Chicago Tribune reported Thursday.
The House voted 83-28 for the proposal. If approved by the Senate, the proposal could go before voters next year.
Sponsoring Rep. David McSweeney, a Republican, said the position is a "luxury" that the cash-strapped state cannot afford, estimating the state could save $1.8 million by eliminating the job.
Provisions of the measure said the attorney general would be the successor if the governor leaves office or dies.
Opponents said the position is needed for a smooth transition in case a governor dies or leaves office and argued lawmakers could cut the position's budget. Gov. Pat Quinn moved from lieutenant governor to governor when lawmakers impeached now-imprisoned Gov. Rod Blagojevich in January 2009.
In a statement, Lt. Gov. Sheila Simon said she is "neutral on the current proposal, as we support the opportunity for the public to provide input in their government through referend[ums]. That said, we are opposed to the idea of abolishing" the lieutenant governor's office.