We consider a possible contribution of mature γ-ray pulsars (with ages of ≥10 5 yrs) to cosmic ray positrons. Within the framework of the γ-ray pulsar outer gap model, e±pairs in the pulsar magnetosphere are produced by the cascade of e±pairs through synchrotron radiation of the return current from the outer gap. A good fraction of these cascade e±pairs are reflected by the hard X-rays from the polar cap via resonant scattering and escape from the pulsar through the light cylinder. The escaped pairs are accelerated to relativistic energies in the pulsar wind driven by low-frequency electromagnetic waves. Using Monte Carlo simulations, we generate a sample of the mature γ-ray pulsars in our Galaxy and calculate the positron production rate from these pulsars. In a simple "leaky box" model, we calculate the ratio of cosmic-ray positrons to total electrons. Our result indicates that the pulsar contribution to the cosmic ray positrons peaks at about 60GeV and the observed e+/(e−+ e+) ratio can be explained in this model.