In view of the difficulty of estimating the shape of extended targets and the low accuracy in multiple extended target tracking in the clutters, a Gamma Gaussian-mixture cardinalized probability hypothesis density filter(GGM-CPHD) which can adaptively estimate the shape of the extended targets is proposed. Firstly, the extension of targets is modeled as an ellipse random hypersurface model, and then it is embedded into the CPHD filter. The extended targets are tracked by its centroid states, the major and minor axis and orientation of ellipse. Simulation for tracking an unknown number of targets in the clutter is made, which shows that the proposed algorithm outperforms the Gamma Gaussian inverse wishart CPHD filter based on the random matrix in estimation of extension’s major and minor axis, as well as centroid states.