The application rate for sprinkler irrigation of water–fertilizer integration machines is an important technical parameter for efficient operation. If the value is too large, the equipment will produce runoff; if it is too small, the equipment will run too long and waste energy. Therefore, it is necessary to provide a feasible scientific and theoretical basis for developing a reasonable application rate. In this study, a mathematical model of soil infiltration for sprinkler irrigation with water and fertilizer integration machines was developed. Soil water accumulation time for different soil’s initial water content, bulk density, sprinkler application rate and soil texture were derived by the finite element method, and these data were used as a training database for the neural network. To make the neural network convenient for predicting the optimal application rate of sprinkler irrigation (the maximum application rate of sprinkler irrigation without runoff) in practice, the time of waterlogging, was multiplied by the optimal application rate of sprinkler irrigation to obtain the total irrigation volume. The optimal application rate of the sprinkler irrigation prediction model of radial basis function (RBF) neural network was constructed with total irrigation water, soil bulk density, initial water content and soil texture as inputs and compared with BP neural network and generalized regression neural network. The highest prediction accuracy of RBF neural network was obtained, and its average relative error was 0.11. To verify the accuracy of the RBF neural network application rate of sprinkler irrigation prediction model in real life, a sprinkler experiment was conducted in the laboratory of Guangzhou University, and the collected soil and lawn of Guangzhou University were used to simulate the actual environment. The results showed that the relative error between the RBF neural network prediction results and the actual values was generally around 10%, while for a total irrigation volume of 58 mm, the optimal application rate of sprinkler irrigation calculated with the model was 42 (mm/h), which can save 70% of irrigation time compared to the case of using the stable infiltration rate of soil as the application rate of sprinkler irrigation without water and fertilizer. Water and fertilizer losses were not observed. This indicates that the model proposed in this study is of practical value in determining the optimum application rate of sprinkler irrigation for water–fertilizer integration machines.