Abstract: The evolution of periodic multiple current sheets in the presence of a pressure anisotropy is numerically simulated based on a two-dimensional three component magnetohydrodynamic method. It is found out that when the plasma parameter β<<1, a slight anisotropy can only expedite the magnetic reconnection process. When the plasma parameter β≈1 （means that the thermal pressure is comparable with the magnetic pressure）, slight perpendicular anisotropy can not only expedite the magnetic reconnection process, but also change the position of X line in reconnection. The magnetic filed changes gradually from an anti-symmetric configuration to a symmetric shape, which will further evolve into an anti-symmetric configuration in opposite phase with initial configuration. Large perpendicular anisotropy or parallel anisotropy will enhance the growth rate dramatically. But the magnetic field configuration does not have fundamental change in parallel anisotropy. There are only some irregular disturbs in the center of the current sheet. The magnetic islands that formed in the anisotropy plasma with periodical current sheets are smaller than those formed in isotropic periodical current sheets with same parameters.