By introducing suitable variables, the Brownian particles motion in a periodic potential with internal time derivative Ornstein-Uhlenbeck noise can be described by a high-dimensional Fokker-Planck equation. The equation can not be solved by the usual small parameter expansion method and potential valley expansion method. An alternative small parameter expansion method is proposed to deal with the equation, and the result is applicable for small potential barrier height, intermediate correlation time and in a larger phase space domain, the approximation can be improved systematically.