In this paper, a new gravity-balanced 3T1R parallel mechanism is addressed. Firstly, structure description, inverse and forward kinematic modeling are performed in detail. Secondly, Jacobian derivation based on screw theory and singularity analysis using Grassmann Line Geometry is performed, and then optimal kinematic design with respect to workspace size, kinematic isotropy and maximum force transmission ratio are conducted. Thirdly, the gravity balancing design using both counterweights and springs is proposed and a prototype of this mechanism is also presented. Results of analysis show that the proposed mechanism has quite a few potential applications.