SB1363 passed on a 34-19 party-line vote Tuesday and now returns to the Senate.
The program was established by the Legislature in 2011 and slightly expanded last year. Only students with a disability, whose parents are in the military or attend very low-performing schools qualify.
The new bill adds kindergartners and also increases funding for students who leave charter schools for private schools.
Just 130 students got the vouchers in 2012 but as many as 5,400 new students a year could qualify if it is signed into law.
The legality of the voucher program is being challenged in court.