This paper proposes a linearized ADMM method to solve inverse problems with generative priors, ie convex objectives subject to non-convex constraints. The constraint is parametrized by a generative model G that is assumed to be differentiable but otherwise highly non-convex. This setting is very relevant in current practice for various linear inverse problems. The proposed linearized ADMM has linear rate which is quite interesting. Overall this paper obtains interesting results for ADMM for nonconvex problems in a novel and relevant setting.