Robotic-assisted therapy is a well-studied method for post-stroke upper limb rehabilitation demonstrating improvements in arm function. The majority of rehabilitation robots are designed for clinical settings to which it is challenging for patients to travel to receive adequate amounts of therapy. One solution is home-based rehabilitation robots which can enable patients to engage with intensive and frequent useful therapy. Nowadays, most home-based upper limb rehabilitation robots promote planar movement, while the motion of upper limb is a three-dimensional movement in daily life. The aim of this paper is therefore, to design and optimize a conceptual design which is suitable for the home environment with three-dimensional movement promotion. Firstly, the mechanical structure of this robot is presented; secondly, the kinematic analysis of this robot is introduced and the workspace is simulated by MATLAB; finally, the topology optimization is used to reduce the robot mass while keeping the strength and stiffness. The total estimated mass of the robot has been reduced from 14.9Kg to 12.5Kg, a reduction of 15.7% of the original design. This research presents a novel lightweight home-based upper limb rehabilitation robot with 4 degrees of freedom, which provides a suitable solution for home-based rehabilitation. This research demonstrates the potential of topology optimization combined with additive manufacturing techniques to reduce the mass of home-based rehabilitation robots a key design requirement.