By making full use of the target size and shape information, a NEET (non-ellipsoidal extended target) JTC (joint tracking and classification) algorithm was proposed on the basis of the star-convex RHM (random hypersurface model). In the proposed algorithm, the target extent state was modeled as star-convex shape. By modeling the target class-related prior information with vector form, constructing its relationship with the simultaneous extent state, and integrating it into the framework of Bayesian filter, the joint processing of tracking and classification was realized. Additionally, two separate vectors were used to model the target state, and the probability update of target class was realized by particle filter based on likelihood function derivation. The simulation results show that the NEET JTC algorithm can accurately classify targets with similar size but different shapes, and improve the target state estimation results when compared with the extended target JTC algorithm based on elliptical shape. The results also show that the proposed algorithm can significantly improve the target state estimation performance when compared with the extended target tracking algorithm based on star-convex RHM.