With the help of an improvement Monte Carlo method, the Berezinskii-Kosterlitz-Thouless phase transition arising in two-dimensional planar rotator model with weak Dzyaloshinsky-Moriya (DM) interaction is investigated. The effects of the DM interaction on specific heat, susceptibility, and magnetization are simulated. The critical temperature of transitions is determined by the so-called Binder cumulant and the susceptibility of finite-size scaling. We find that the chiral Z2 symmetry reduced by the DM interactions plays an important role in a two-dimensional XY spin system,typically, the critical temperature is sensitive to weak DM spin couplings.