Abstract: In this article, the authors show the existence of global solution of two-
dimensional viscous Camassa-Holm (Navier-Stokes-alpha) (NS-α) equations. The authors also prove that the solution of the NS-α equations converges to the solution of the 2D NS equations in the inviscid limit and give the convergence rate of the difference of the solution.

Key words: inviscid limits, Navier-Stokes-α model, Camassa-Holm equations