With a rapid development of electric vehicles (EVs), the spatial and temporal charging load prediction of EVs provides support for the construction of charging stations and the planning and construction of charging facilities. Therefore, this paper proposes a method of electric vehicle load demand analyzing based on the principle of maximizing the utility. Firstly, the temporal and spatial distribution of electric vehicle is established based on trip chain. Then, a choice is decided to imitate the charging behaviors of users based on the principle of utility maximization and time cost method. Finally, the electric vehicle temporal and spatial charging load demand is forecasted. The effectiveness and correctness of the proposed method is verified by contrasting with related literature, and simulations analyze the impact of permeability and charging stations location on charging load. The results show that the charging load is also increased as the permeability increased; Reasonable layout of charging station position will make charging load more evenly.