In recent years, electric vehicles have attracted significant attention due to environmental issues. Charging stations installation requires a systematic consideration of relevant issues such as determination of the location and size of charging stations. On the other hand, it is necessary to encourage private investors to invest in charging stations installations and to provide proper conditions for them so that they can profit from their investment. In this paper, the fast charging station (FCS) planning problem is modeled as a mixed integer nonlinear programming (MINLP), in which the objective function of distribution company (DISCO) and FCS owner (FCSO) have been considered, separately. In the proposed model, the location and size of FCSs as well as the price of transacted energy between DISCO and FCSO are determined, such that the objective functions of DISCO and FCSO are optimized. In the proposed method, queuing theory and user equilibrium based traffic assignment model are used to determine the size of FCSs. Then, the problem of multi-objective planning of FCSs has been investigated, considering the objectives of DISCO and FCSO. In addition, the final solution is chosen from the Pareto front solutions based on the economic and operational indices. Finally, the efficiency of the proposed method is demonstrated by numerical results.