Fault tolerance is essential for quadruped robots when they work in remote areas or hazardous environments. Many fault-tolerant gaits planning method proposed in the past decade constrained more degrees of freedom(DOFs) of a robot than necessary. Thus a novel method to realize the fault-tolerant walking is proposed. The mobility of the robot is analyzed first by using the screw theory. The result shows that the translation of the center of body(CoB) can be kept with one faulty actuator if the rotations of the body are controlled. Thus the DOFs of the robot body are divided into two parts: the translation of the CoB and the rotation of the body. The kinematic model of the whole robot is built, the algorithm is developed to actively control the body orientations at the velocity level so that the planned CoB trajectory can be realized in spite of the constraint of the faulty actuator. This gait has a similar generation sequence with the normal gait and can be applied to the robot at any position. Simulations and experiments of the fault-tolerant gait with one faulty actuator are carried out. The CoB errors and the body rotation angles are measured. Comparing to the traditional fault-tolerant gait they can be reduced by at least 50%. A fault-tolerant gait planning algorithm is presented, which not only realizes the walking of a quadruped robot with a faulty actuator, but also efficiently improves the walking performances by taking full advantage of the remaining operational actuators according to the results of the simulations and experiments.