A novel spatial parallel robotic mechanism with three degrees of freedom (DOF) was proposed, whose moving platform of the mechanism had two-translational and one-rotational DOF. Based on the screw theory, kinematics output property and mobility of the manipulator were analyzed, respectively, and analytical solutions of position and velocity for both direct and inverse kinematics were derived. Furthermore, the singularity and the dexterity were discussed. Since the Jacobian matrix, mapping the input velocity vector space into the output, is an identical matrix, the present mechanism is a free-singularity fully-isotropic one, which has good performances in motion and force transmission and potential applicable future.