Numerical simulation of a parabolic-shaped pulse pair propagating in fiber is done based on the nonlinear Schrdinger equation, and the solution of the equation is found with split-step Fourier method. The transmission behaviors of the parabolic-shaped pulse pair in single-mode fiber and dispersion-managed fiber are studied. Simulation results show that there is almost no interaction between the parabolic-shaped pulse pairs transferring in fiber, and the main challenge is to preserve their shape and reduce the interference generated by pulse stretching. The evolution of parabolic-shaped pulses in fiber is affected by dispersion. When the pulses propagate in normal dispersion fiber or dispersion-managed fiber with average normal dispersion, they can maintain the parabolic shape. Especially, the pulses stretch fiercely when propagating in normal dispersion fiber, and taking advantage of the dispersion management methods, the tendency of pulse stretching is suppressed well. This result is of great help in long-haul optical fiber communication without relay.