Mid-spatial-frequency (MSF) errors seriously damages the imaging performance of optical components. Path pattern is an important factor that affects the generation of MSF waviness in polishing. This paper proposes a versatile pseudo random tree-shaped path (RTSP) generation method imitating the growth rules of tree branch in nature, which can efficiently generate continuous, uniformly distributed and multi-directional paths on a specified surface. Furthermore, the effectiveness of RTSP to suppress MSF waviness is verified by numerical simulation and experimental results. Finally, the RTSP is applied to the polishing of Ti-6Al-4V titanium alloy mirror. Results indicate that grinding marks have been significantly removed, while no obvious MSF waviness is introduced.