Stumbo said he planned to file the bill on Tuesday, the first day of the 2015 legislative session.
The bill would require doctors to be trained before they could prescribe the drug to patients.
And Stumbo said the state would have a strict oversight system in place to make sure prescriptions were not abused.
State lawmakers have softened their stance toward the cannabis plant in recent years. Last year, the state harvested its first hemp crop in decades and the state Legislature approved a bill allowing researchers to experiment with cannabidiol.
Stumbo said he filed the bill because he believes lawmakers need to discuss the issue.
(Copyright 2015 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.)