We designed a distributed charging coordination method for electric vehicles over a multi-time interval with the so-called progressive second price (PSP) auction mechanism which was proposed by Lasar and Semret in order to efficiently allocate the divisible resources among multi agents. The incentive compatibility holds for the auction games under the PSP mechanism. However due to the cross-elastic correlation among the different charging instants, the marginal valuation of an individual agent at each instant is determined by both the demand at this instant and the total demand at the whole interval. This phenomena makes the underlying auction games distinct from those studied in the literature. As a main contribution of the paper, we showed that the efficient bid profile over the multi-time interval is a Nash equilibrium of the auction systems.