Aiming at the problem of fault estimation in a class of time-varying discrete switched system with arbitrary sequence, in this paper we propose a novel fault estimation algorithm. The algorithm uses the introduced virtual fault signal to construct fault estimator, and uses the residual signal to modify the introduced virtual fault step by step through using the iterative learning method and making the virtual fault gradually approach to the actual fault by increasing the iterative number. The convergence of the algorithm in each subinterval is strictly proven by the use of contraction mapping method, and the convergent condition of the algorithm is provided. Theoretical analyses indicate that the proposed algorithm can estimate different types of faults occurring in a switched system accurately in a finite interval. Finally, the validity of the algorithm is verified by simulations.