In this paper, using finite element method, a Back-Gated metal-semiconductor-metal photodetector is numerically modeled and compared with the experimental results. To do this, the time-dependent continuity equations coupled with Poisson's equation have been scaled down, discretized in two space dimensions, and solved for n(n), n(p), and phi variables by the Galerkin method. The I-V characteristics of this photodetector are obtained to check the validity of our calculation. The transient response of the device and their FWHM are calculated at different negative voltage applied to the back-gate. We found that the transient response of the BGMSM photodetector is highly sensitive to the beam position and, also, the FWHM is decreased with increasing the back-gating voltage. Besides, the electrostatic potential, electron, and hole number of densities profiles are numerically presented.