Abstract: The construction method of slip surface is one of the key issues in slope stability analysis, and it is a challenging work to construct slip surface with complex shape. The curve constructed based on the integral of Logistic function and other basis functions can take the place of the traditional slip surface constructed by non-circular curves, which can not only improve the smoothness of the slip surface but also reduce its degree of freedom. The slip surface construction methods based on basis functions are sorted out in this paper. They are divided into the construction methods based on the superposition of continuous functions and the methods based on integral operation. The characteristics of Logistic function and its integral are carefully investigated, and the influence of different parameters on the shape of the curve is obtained to narrow the value range of relevant parameters. It provides a basis to reduce the degree of freedom of slip surface. On this basis, a method to determine the initial values of a given slip surface parameters is also presented. The calculation results of two slope examples show that the proposed method is tolerably well in slope stability analysis.