The quadruped robot, which is designed according to the morphology of quadruped mammal, can adapt to the complex terrain with its superior movement property. In view of the importance of motion control required for the quadruped robot, a research has been made of the jump control issue in the movement process of quadruped robots. Firstly, a spring-loaded inverted pendulum model (SLIP) is used to simplify the structure of the quadruped robot, thus establishing the dynamics equation of the simplified model, followed by an analysis of the motion process of the model and the conversion conditions between landing and airborne phases. Secondly, the SLIP dynamics model is to be established in the simulation platform, and the simulation sample data is to be obtained through the dynamics simulation, with a neural network trained by using the sample data, in which the energy consumed by collision and damping in the contact process between the quadruped robot and the ground is to be taken into account. Finally, given the initial height and horizontal velocity of the model, the appropriate landing angle is calculated through the neural network, thus obtaining the expected final horizontal velocity and the bounce height as well. The experimental results show that the method based on the neural network can improve the control accuracy of the SLIP model.