The dephasing time of a positron in the total field associated with a laser pulse in a plasma is studied numerically.It is shown that the dynamics of the positron is quite different from that of an electron due to the electrostatic potential in the body of the pulse. The dephasing time of the positron increases with the pulse length and decreases with the pulse intensity nonlinearly. In the long pulse case (L> λp) the dephasing time is proportional to the pulse length. These results provide a scientific basis for experiments to observe the positron acceleration scheme, and may be important to the physics of laser-particle interactions in multi-component plasmas.