The trend of high-speed optical communication is to realize large capacity, fast speed and long haul transmission. However, the dispersion in an optical fiber link can cause signals distortion or even inter symbol interference (ISI). With increasing signal rate and transmission distance in the optical communication system, the development of high-speed optical fiber communication is restricted seriously. This paper is focusing on the dispersion characteristics and compensation of the polarization multiplexing (POLMUX) coherent optical communication system: (i) to study on dispersion theoretically, e.g., chromatic dispersion (CD), polarization mode dispersion (PMD) and dispersion tolerance; (ii) to analyze and compare the performance of dispersion with various 16-ary modulation formats; (iii) to compensate dispersion by the classical dispersion compensation methods.