The traditional locomotion paradigm of quadruped robots is to use dexterous (multi degrees of freedom) legs and dynamically optimized footholds to balance the body and achieve stable locomotion. With the introduction of a robotic tail, a new locomotion paradigm becomes possible as the balancing is achieved by the tail and the legs are only responsible for propulsion. Since the burden on the leg is reduced, leg complexity can be also reduced. This paper explores this new paradigm by tackling the dynamic locomotion control problem of a reduced complexity quadruped (RCQ) with a pendulum tail. For this specific control task, a new control strategy is proposed in a manner that the legs are planned to execute the open-loop gait motion in advance, while the tail is controlled in a closed-loop to prepare the quadruped body in the desired orientation. With these two parts working cooperatively, the quadruped achieves dynamic locomotion. Partial feedback linearization (PFL) controller is used for the closed-loop tail control. Pronking, bounding, and maneuvering are tested to evaluate the controller’s performance. The results validate the proposed controller and demonstrate the feasibility and potential of the new locomotion paradigm.