A dispersion equalizer is designed to compensate dispersions of polarization multiplexing coherent fiber optics communication systems. The proposed equalizer is realized with fraction spaced butterfly finite impulse response (FIR) structure and the corresponding adaptive algorithms are least mean square (LMS) and recursive least squares (RLS), respectively. The residual chromatic dispersion(CD) and polarization mode dispersion (PMD) tolerances of both algorithms are analyzed by simulation. The simulation results show that RLS can compensate 1760 ps/nm residual CD and 104.9 ps differential group delay (DGD) simultaneously and it has 2.23 dB promotion than LMS.