The problem of optimal planning of plug-in electric vehicle (PEV) charging stations is studied. Different from many other works, we assume the station investor to be a new private entrant into the market who intends to maximize its own profit in a competitive environment. A modified Huff gravity-based model is adopted to describe the probabilistic patronizing behaviors of PEV drivers. Accordingly, a bi-level optimization model is formulated to decide not only the optimal site and size of the new charging station, but also the retail charging prices in the future operation stage. Based on the specific characteristics of the problem, the operation level sub-problem is reformulated to a convex programming and an efficient solution algorithm is designed for the overall bi-level optimization. Numerical examples of different scales demonstrate the effectiveness of the proposed modeling and computation methods, as well as the importance of considering the competitive effects when planning the charging station.