Poly[methyl methacrylate(81)/butyl acrylate(19)] copolymer was exposed to atmosphere of humidity for various times. The normal alpha and rho peak, a third LL peak is observed in thermally stimulated depolarization current (TSDC) spectra of the copolymer. The alpha peak corresponds to the glass transition, the rho peak originates from the detrapping of trapped carriers in the bulk amorphous structure, and the LL peak can be attributed to the charge detrapping related to the liquid-liquid transition of the copolymer. The three peaks all move to lower temperature with an increase of the moisture content, indicating that the flexible moisture content not only has an effect of plasticization on the glass transition and liquid-liquid transition, but also makes the trap depth of rho peak shallower. The trap depth of rho peak is affected by the introduction of moisture content and the degree of hydration of the copolymer. Based on analysis of calculated results, it was confirmed that the relaxation time of LL peak obeys VF equation when temperature is below T (LL).