We consider a  nonsmooth optimization problem on Riemannian manifold, whose objective function is  the sum of a differentiable component and a nonsmooth convex   function.  We first reformulate this problem  to a separable form,  and the propose a manifold inexact augmented Lagrangian method for the separable problem.  Theoretically,  the convergence to critical point of the proposed method is established under some mild assumptions.