In recent years amorphous silicon solar cells have been receiving a great deal of interest due to their high energy conversion efficiency and low cost. The positions of absorption peak reflect the good absorption performance at specific frequency point or nearby spectra. However, the absorption peaks of amorphous silicon solar cell which are mainly determined by the properties of amorphous silicon and metal electrode, cannot be tuned. And the absorption efficiency can not be further enhanced also. Therefore, monolayer graphene film will be employed in the solar cells with periodic structure due to its remarkable electro-optic properties. With a suitable chemical potential applied, the dielectric constant of graphene can be tuned. This design mainly aims to tune the position of the absorption peak based on the graphene by using finite-difference frequency-domain method. Also, an approximate fitted function is developed in order to overcome the singularity in the exact expression. Numerical results show that the approximate closed form expression generates results within a maximum absolute error of 0.8%. Theoretical results provide the realistic organic thin-film solar cells with theoretical basis and technical support.