Mathematical model is an important way to understand and control the spread of infectious diseases. In this paper, cubic B-spline quasi-interpolation method is used to solve a kind of dengue fever model with vertical transmission and time period. Firstly, the basic theory of cubic B-spline quasi-interpolation is introduced. Secondly, the derivative of the quasi-interpolation is applied to approximate the spatial derivative of the dependent variable, and the modified Euler method is used to approximate the time derivative of the dependent variable to obtain a numerical scheme. Finally, the numerical simulation diagrams and the numerical solutions are obtained  when the basic regeneration number of the dengue fever model is greater than 1 and less than 1.