A new partially blind signature scheme is proposed based on Schnorr blind signature scheme. Compared with the previous schemes, the proposed scheme has lower computations and shorter signature size. By conversely using the proposed partially blind signature, a fair e-payment protocol is given. An advantage of this protocol is that two participants achieve the goals of exchanging their items without intervention of a third party. The low computations and good properties of the underlying partially blind signature guarantee that the proposed protocol has needed efficiency and security.