To effectively mitigate the impact of wind power output variability on grid operation, an improved cumulant probabilistic load flow calculation method using the Gaussian function-maximum entropy principle is proposed for a wind power integration system. First, taking the Gaussian function as the carrier of wind speed distribution information, a probabilistic model of wind power output accounting for the boundedness of wind speed is developed using an improved reflectance kernel density estimation. This model can accurately derive numerical characteristics such as moments and cumulants of each order describing the stochastic nature of the wind power output. Second, based on the numerical characteristics of state variables such as node voltage and branch power, the Gaussian function is used to improve the maximum entropy model into the distribution expansion of state variables. The influence of wind speed distribution shape of the input side on the state variables distribution of output side is taken into account by using the number and the feature of Gaussian function. Concurrently, the constraint form of the enhanced maximum entropy model is transformed to an algebraic from an integral, boosting computational efficiency. Finally, the proposed method is tested with the IEEE30-bus system, and the results demonstrate the effectiveness and accuracy of the proposed method.