We investigate the equilibrium property of a mesoscopic ring with a spin-orbit interaction. It is well known that, for a normal mesoscopic ring threaded by a magnetic flux, the electron acquires a Berry phase that induces a persistent (charge) current. Similarly, the spin of an electron acquires a spin Berry phase when traversing a ring with a spin-orbit interaction. It is this spin Berry phase that induces a persistent spin current. To demonstrate its existence, we calculate the persistent spin current without an accompanying charge current in the normal region in a hybrid mesoscopic ring. We point out that this persistent spin current describes the real spin motion and can be observed experimentally.