Rational utilization of demand side resources is one of the effective ways to delay distribution network planning and promote wind power consumption. However, the uncertainty of demand response (DR) will have an important impact on distribution network planning. In order to analyze the impact, firstly, in view of the uncertainty of user participation in demand response, the fuzzy model of user response under the time-of-use (TOU) price mechanism is introduced, and the change mechanism of user response rate error is explained. Then, based on the user response fuzzy model, a distribution network fuzzy credibility constraint planning model considering the uncertainty of DR is established; considering the problem that the traditional fuzzy simulation combined with deterministic power flow calculation is inefficient for verifying the credibility constraints, a genetic algorithm with built-in incremental power flow and fuzzy simulation is proposed, reducing the difficulty of solving the model. Finally, the risk assessment indices for the power flow limit violation of the distribution network are established to evaluate the impact of the uncertainty of DR on the safety of the distribution network. Simulation cases show that the proposed model and algorithm can effectively improve the security of distribution network planning, and reduce the risk of exceeding the limits of node voltage and branch power caused by the uncertainty of DR.