A two-dimensional model of a metal-semiconductor-metal (MSM) ZnO-based photodetector (PD) is developed. The PD is based on a drift diffusion model of a semiconductor that allows the calculation of potential distribution inside the structure, the transversal and longitudinal distributions of the electric field, and the distribution of carrier concentration. The ohmicity of the contact has been confirmed. The dark current of MSM PD based ZnO for different structural dimensions are likewise calculated. The calculations are comparable with the experimental results. Therefore, the influence with respect to parameters s (finger spacing) and w (finger width) is studied, which results in the optimization of these parameters. The best optimization found to concur with the experimental results is s = 16 \mu m, w = 16 \mu m, l = 250 \mu m, L = 350 \mu m, where l is the finger length and L is the length of the structure. This optimization provides a simulated dark current equal to 24.5 nA at the polarization of 3 V.