Connecting distributed photovoltaic (PV) to the distribution network through the grid-connected micro grid is one of effective ways to solve large-scale distributed PV integration problem. Taking the gird-connected PV micro gird with the energy storage system and demand response resources as the study object, this paper studies the optimal allocation strategy of energy storage system in PV micro grid considering uncertainty of price-based demand response (DR). Firstly, the impacts of price-demand elastic curve and based load uncertainty on the price-based DR uncertainty are considered, and the price-based DR fuzzy response model is established. Based on the price-based DR fuzzy response model, the price-based DR fuzzy chance optimal operation model, which is to minimize the difference between the system load and the PV output, is proposed. After that, based on the optimal results of the optimal operation model, the optimal allocation model of the energy storage system in grid-connected PV micro grid is established based on the fuzzy chance constrained program. By transferring the fuzzy chance constrains into their clear equivalents, the fuzzy chance optimal problem can be converted to a deterministic optimal problem to solve. Finally, the simulation results verify the validity of the proposed model. This work is supported by National Key Research and Development Program of China (No. 2017YFB0903601), National Natural Science Foundation of China (No. 51777088) and Science and Technology Project of State Grid Corporation of China (No. SGHADK00PJJS1500060).