To the issue of joint estimation of the extended targets shape and kinematic state,a Gaussian mixture PHD filter based on star-convex Random Hypersurface Models (RHM) is proposed for extended target tracking.The proposed algorithm describes the extension of measurements by the star-convex RHM and uses the sampling constraint to limit the shape parameters of targets.Then,under the Gaussian mixture probability hypothesis density framework,the extended targets are tracked by calculating and updating the likelihood and new information.Simulation results show that the proposed method can guarantee the availability and feasibility of the tracking and improve the accuracy of extended target kinematic state and shape estimation.