In this work, a quadruped robot designed for trotting gait with compliant leg is proposed. Based on the Spring-Loaded Inverted Pendulum model (SLIP), simplified models of different degrees of freedom (DOF) of the robot body are constructed. Under the analysis of the dynamics model, a simple running control method was implemented to decouple six DOF of the body, which requires minimal task level feedback and only controls the leg torque and touch down angle. In simulation this control method successfully executes on robot running from stationary to a constant speed when climbing up or down slope with well regulated pitching, rolling and yawing motions. Additionally, a prototype robot is constructed, and the control method is verified by prototype experiment in the sagittal plane.