Senate Majority Leader Chip Rogers (R-Woodstock) said Wednesday he is introducing legislation that would use taxpayer money to send the students to private schools.
The state government already gives such vouchers to families with special-needs students under a program that started in 2007.
About 2,100 students in Georgia are receiving the vouchers.
"We think this is the next logical step in providing choice to children and their parents," Rogers said during a news conference at the state Capitol.
Rogers' bill would increase the per-student funding from $6,331 to about $9,800 for special needs students.
Military students and foster care children would get between $5,000 and $9,000 each, depending on where they go to school and how old they are.
Critics say the bill would take money away from public schools at a time when funding is scarce.
"It's an incremental attack on public schools," said Sen. Vincent Fort, a Democratic member of the Senate Education and Youth Committee. "We need to put our resources into public schools instead of taking money away."
The bill also would allow parents to enroll in the voucher program four times a year rather than just once per year. Parents have complained that if they miss the window to sign up, their children are stuck in a school for a full year.
In addition, the bill would set up deadlines for when the state Department of Education should send payments to private schools. Some schools have said the payments are often late because the state has just one person running the voucher program.
Last year former Senate President Pro Tem Eric Johnson, a Savannah Republican, failed to get legislation passed that would create a universal voucher program in Georgia, which would give a voucher to any student in the state to attend the school of their choice. Johnson resigned his seat last year to run for governor.
National experts say just six states and Washington, D.C., have voucher programs for low-income or special-needs students. No state has successfully passed a universal voucher program.