The nature of single particle classical phase space trajectories in Rindler space with non-hermitian PT-symmetric Hamiltonian have been studied both in the relativistic as well as in the non-relativistic scenarios. It has been shown that in the relativistic scenario, both positional coordinates and the corresponding canon- ical momenta are real in nature and diverges with time. Whereas the phase space trajectories are a set of hyperbolas in Rindler space. On the other hand in the non- relativistic approximation the spatial coordinates are complex in nature, whereas the corresponding canonical momenta of the particle are purely imaginary. In this case the phase space trajectories are quite simple in nature. But the spatial coor- dinates are restricted in the negative region only.