A novel type of photodetector structure based on graphene nanoribbons (GNR-PD) array was presented and the analytical device model was discussed in this paper. By applying the two-dimensional Poisson equation, the model of GNR-PD analytical device model was established under the weak nonlocal approximation condition. The I-V characteristics and photoresponse characteristics of GNR-PD device are derived. It is shown that due to the extra-high quantum efficiency and photoelectric gain of GNR-PD, the photo responsivity of up to 150 A/W or more can be obtained.