In order to control the horizontal body position of a trotting hydraulic quadruped robot, an approximated dynamical model was built based on the motion decomposition along the support line, which simplifies the body and the stance legs to a seven-link mechanism and a linear inverted pendulum. A calculation method for landing positions of swing feet was proposed based on the analytic solution of the linear inverted pendulum model. It was realized to control the horizontal position of the body. For the velocity limitations of the hydraulic cylinders pushing and pulling, an optimization problem for the joint angular velocities was formatted as a QP problem, and a QP solver was designed to decrease the demands for the joint angular velocities. In comparison to the conventional pseudoinverse optimization algorithm, the proposed algorithm could avoid the singular state of the leg more effectively. The simulation and experiment results show that the desired horizontal body position trajectories can be tracked accurately by using the proposed algorithms, even the joint angular velocities being limited.