Based on a new type of two-level-system reservoir, we investigate the impact of dissipation on Berrys phase of a spin trapped in a periodical exteal field. It is found that the existence of environmental noise could lead to a decaying term in the matrix of Berrys phase as the sign of a decoherence process, which is in agreement with the result of Nazir et al. (Phys. Rev. A 65 (2002) 042303). Particularly, in comparison with a specialized case of the traditional Leggett dissipation model, we only shows the dependence of time but not temperature in decaying term. A concrete case is exhibited by using the one-dimensional Ohmic function.