This paper presents a new trajectory Poisson multi-Bernoulli (TPMB) filter for group target tracking. Due to the collective behavior and dense spatial distribution, exact trajectory estimation is an extremely challenging task in group target tracking. Aiming for improved performance in group trajectory estimation, the virtual leader-follower model is incorporated into the standard TPMB filter in this paper to address the coordinated motion within groups. Moreover, the Gaussian implementation and $\boldsymbol{L}$-scan approximation for the proposed group target trajectory PMB (GTTPMB) filter are also provided. Finally, a simulation scenario with splitting and merging of groups is established to evaluate the proposed GTTPMB filter. The results demonstrate that the proposed filter can effectively estimate the trajectories of group members without introducing additional computational burden.