This paper describes the mechanical configuration of a quadruped robot firstly. Each of the four legs consists of three rotary joints. All joints of the robot are actuated by linear hydraulic servo cylinders. Then it deduces the forward and inverse kinematic equations for four legs with D-H transformation matrices. Furthermore, it gives a composite foot trajectory composed of cubic curve and straight line, which greatly reduces the velocity and acceleration fluctuations of the torso along forward and vertical directions. Finally, dynamics co-simulation is given with MSC.ADAMS and MATLAB. The results of co-simulation provide important guidance to mechanism design and parameters preference for the linear hydraulic servo cylinders.