It is shown that by numerical simulation, pre chirped picosecond optical pulse can transmit stably in full dispersion compensation optical fiber links considering not only second, but also third order dispersion compensation using dispersion shift fiber with opposite dispersion signs; it eliminates waveform distortion and peak shift due to the third order dispersion. The optimal pre chirp is relevant to second order dispersion map. During each compensation optical fiber link, pulse width, chirp and peak shift vary around their initial values. It demonstrates that the pre chirp and high order dispersion compensation are two key elements at high bit rate transmission system.