Let X be a compact metric space and f : X → X be a homeomorphism map. In this paper we are going to introduce the h-average shadowing property for discrete dynamical system (X, f). It is shown that f has the h–average shadowing property if and only if f−1 has the h–average shadowing property. We also prove that if f has the h-average shadowing property, then every point x is chain recurrent. The relation between chaos and shadowing property in discrete dynamical system is considered.