Abstract: The generalized triangular prism (GTP) voxel designed for the borehole data is the commonly method in the geological modelling, and it can be used to build the 3D solid geological model to express the stratigraphic space through the adjacent GTP voxel based on the borehole sampling data. Its accuracy is lower, and the stratigraphic surface is non-smooth when the interval of the adjacent borehole is long, so the theory and method of interpolation and smoothing of the GTP 3D geological model is proposed, which can interpolate the GTP model adaptively but not change the model structure. The main content is as follows: (1) The definition of GTP model smoothness and the relevant method are proposed to measure the smooth degree of the GTP model, which is used to deicide whether the GTP voxel needs interpolation. (2) The design of virtual boreholes and the corresponding method for the interpolation of the GTP geological model according to the GTP geometric smoothness are discussed. (3) The interpolation method for the adaptive GTP geological model based on the design and calculation of the virtual boreholes, can be studied based on the existing GTP building method.