A Gaussian mixture PHD filter for extended target tracking based on star-convex random hypersurface model was proposed for the problem of joint estimation of the extended target shape and motion state. The proposed algorithm modelled the diffusion degree of measuration by using the star-convex random hypersurface model. Then, the extended targets were tracked by calculating and updating the measurement likelihood and innovation under the Gaussian mixture probability hypothesis density framework. The simulation results showed that the proposed method could guarantee the tracking availability and feasibility and improve the estimated accuracy of extended target motion state as well as the target shape. Keywords: star-convex; random hypersurface model; extended target; Gaussian mixture probability hypothesis density