This paper mainly focuses on the wheel-legged vehicle which consists of thirteen rigid bodies with a total of eighteen degrees of freedom. And it proposes a control method for the wheel-legged vehicle, which is a multi-rigid-body system. Firstly, by using space vectors, the kinematics of the wheel-legged vehicle is modeled, which is used as the basis for the multi-rigid-body dynamics model. In order to simplify the derivation process, this paper uses the concept of kinematic tree and presents the whole recursive process through pseudo-code. The multi-rigid body dynamics model can only respond to the relationship between joints and motions, but the wheel-legged vehicle has a strong interaction with the external environment. It is necessary to introduce the virtual model control (VMC), which combines the kinematic state of the wheel-legged vehicle with the ground contact reaction force by four Spring-damped virtual components. Solving the external force by using VMC can simplify the derivation process and it works well. By using the wheel model, the contact force can be transformed into what the multi-rigid body dynamics model needed when calculates the joint torques.