All over the world, the attention on the exploitation of public research, which is mainly implemented by technology transfer, has increased in recent years. Licensing, which is one of representative mechanisms for public-to-private technology transfer, is accompanied by the frequent conflicts in negotiating a license payment between public research institutes (PRIs) and private firms. In spite of the body of literature on technology transfer in a licensing context, it focuses on contracts between private firms. Even the existing literature, which addresses public-to-private technology transfer through licensing, to our knowledge, has not yet formalized an established licensing model. This paper develops a mathematical model of public-to-private licensing, not hitherto tried by academics. The model addresses important issues to be applied comprehensively in licensing practice, such as determining a royalty rate, balancing between an initial payment and a running royalty, designing an inventor's incentive system, and setting a minimum payment as a screening criterion. The paper also provides reasonable management implications to controversial issues in technology transfer from PRIs to private firms, partly employing the comparative analysis between current stylized licensing practice and the one suggested in the model. We hope that study contributes to providing the foundation on which the theory on public-to-private licensing would extend to an in-depth level.