This paper investigates the problem of robust fault estimation for a class of uncertain networked control systems (NCSs) with random communication network-induced delays, which are to be modeled by the Markov processes. Based on the Lyapunov-Razumikhin method, a delay-dependent fault estimator is obtained in a form of bilinear matrix inequalities, irrespective of the uncertainties and network-induced delays. An iterative algorithm is proposed to change this non-convex problem into quasi-convex optimization problems, which can be solved effectively by available mathematical tools.