The measure cleared committee Wednesday evening and now heads to the full chamber. It had passed the House last week.
Rep. Kelly Cassidy sponsors the bill which gay and lesbian advocates support. The Chicago Democrat says conversion therapy can increase the risk of suicide and "mental anguish" in teenagers struggling with their sexuality.
The initiative would prevent mental health providers from using the treatment on anyone under the age of 18.
Just last year, the House defeated a similar Cassidy plan 44-51 - with 22 members not voting. California, New Jersey and Washington, D.C. have enacted bans of conversion therapy.