In this article, we investigate the behaviors of Einstein-Podolsky-Rosen (EPR) steering for two uniformly accelerated atoms coupled with electromagnetic vacuum fluctuation. We firstly analyze the solving process of master equation that describes the system evolution. Unlike the complicated behaviors of entanglement, EPR steering decays with decoherent time and presents sudden death, the critical points of which can be located. In addition, small acceleration and interatomic distance can decrease the degradation of EPR steering. Since the measure of EPR steering adopted in this paper is equivalent to that of Bell non-locality, the EPR steering dynamics discussed in the article is applied equally to Bell non-locality.