For some manipulation tasks needing to change objects’ orientation and position quickly, a hybrid robot, consisting of a 4-DOFs SCARA and a 3-DOFs (2R1T) parallel wrist, is presented. First, the swing and translation characteristics of the parallel wrist are quantitatively analyzed by numerical method, and its maximum swing angle and optimum working curve are obtained. A swing-rotation method for representing the attitude of the parallel wrist is proposed, and it can be transformed with the commonly used Azimuth-Swing method, which is the key to decouple kinematics of hybrid robots. Then, the singularity of the mechanism, when its attitude expressed by the proposed method, is also analyzed. The forward and inverse kinematic equations are derived in an analytical form. Finally, the kinematics simulation based on ADAMS verifies the correctness of the robot kinematics.