The evolution of sum-chirp for an initially chirped Gaussian pulse is studied in the polarization multiplexed communication system, with fibre attenuation considered. The sum-chirp is found to have the character of saturation.Its value appears different along the two different polarization axes, determined by the incidence polarization angle. We also find that sum-chirp is dominated by the initial chirp at a short distance, and by the cross-phase modulation effect at long distance. And it is influenced apparently by a wavevector mismatch parameter below 10 ps/km. Further, its saturation results from the effective distance determined by fibre attenuation.