The trajectory probability hypothesis density filter (TPHD) is capable of producing trajectory estimates in first principle without adding labels or tags. In this paper, we propose a new TPHD filter referred as MM-TPHD for jump Markov system (JMS) model that the highly dynamic targets movement switches between multiple models in multi-trajectory tracking. Firstly, we extend the concept of JMS to the multi-trajectory scenario of maneuvering target and derive the TPHD recursion for the proposed JMS model. Then, we develop the linear Gaussian Mixture (LGM) implementation of MM-TPHD recursion and also consider the L-scan computationally efficient implementations. Finally, simulation results in maneuvering multi-trajectory tracking demonstrate the performance of the proposed algorithm.