Abstract: In order to explore the effects of the initial first-order phase modulation on the long distance propagation properties of Gaussian optical pulses in optical fibers, evolutions of initially first-order phase modulated Gaussian optical pulses in terms of their shapes, amplitudes, and temporal trajectories, were numerically investigated by starting from the nonlinear evolution equation governing the optical pulse propagation and using the split-step Fourier algorithm. The results show that, the Gaussian pulses exhibit damped oscillation behavior in terms of their amplitudes on the one hand and shift towards the leading or trailing edges of the pulses along straight lines in terms of their temporal trajectories on the other hand due to the first-order phase modulation. The shifting magnitude and direction respectively depend on the absolute value and sign of the phase modulation parameters. This work can extend study on long distance propagation properties of non-soliton pulses. Moreover, it can also be applied in straight-line manipulating of temporal trajectories.