Quadruped robots can mimic animal locomotion mode and have great potential usage in unstructured environments. However, as mobile platforms, quadruped robots often lack manipulation capabilities. In this project, we equipped the quadruped robot SDU-ADog with a torque-controlled 6-DOF arm. A novel control framework which combines virtual model control (VMC) and prioritized whole-body control (WBC) for the whole system is proposed in this paper. VMC finds optimal target ground reaction forces while compensating the arm’s inertia, and then makes the robot compliant to external disturbance. Prioritized WBC deals with multiple tasks in an optimal fashion and achieves efficiency and robustness of robot’s locomotion and manipulation. The effectiveness of our framework has been evaluated through a set of robot dynamic simulations conducted in Webots. The robot can finish balance maintaining with moving arm, fixed point tracking while trotting, and locomotion over different obstacles with an end-point task. •We devise a control framework for legged mobile manipulators which considers the full kinematics and dynamics model of the robot.•We stabilize the robot’s CoM position and orientation by combining VMC and WBC.•We validate the method’s robustness by simulations of fixed-point tracking while trotting over obstacles.•The robustness is further validated by experiments on our robot. The results show that our control frame work is valid and easy to transfer from simulation to reality.