In this paper, based on the theoretical model of optical wave propagation in the parity time symmetric waveguide, the propagation characteristics of bright solitons in the Rosenmorse potential are studied numerically. The refractive index distribution of the parity-time symmetric waveguide has a linear focusing effect for beam, and the gain/loss distribution can cause the transverse energy-flow of beam. The results show that when the modulation depth of refractiveindex is positive, the first-order bright solitons can propagate and form a wavy beam in the waveguide. When the modulation depth is negative, the first-order bright soliton splits into two beams. One beam disappears and the other beam travels forward ata certain speed. The modulation depth of gain/loss can affect the propagation behavior of two beams. The second-order bright soliton can propagate and form a stable breathing beam under a lower modulation depth of the gain/loss. The third-order bright soliton appears splitting and converging periodically during the process of transmission. The fourth-order and higher order bright solitons cannot propagate stably in the waveguide. The results can provide a theoretical basis for the application of parity time symmetry in optical waveguides.