  In this paper we consider the inviscid limit for the periodic solutions to
Navier-Stokes equation in the framework of Gevrey class. It is shown that the
lifespan for the solutions to Navier-Stokes equation is independent of
viscosity, and that the solutions of the Navier-Stokes equation converge to
that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover
the convergence rate in Gevrey class is presented.
