The relative coupling efficiency of top two-dimensional metal coupling grating for mid-wave quantum well infrared photodetector is calculated by finite difference time domain algorthms. The relative coupling efficiency with respect to the grating parameters, such as grating period, duty ratio, and grating depth, is computed. The calculated results show that the relative coupling efficiency will reach the largest value for the 4.1 μm incident infrared light when taking grating period as 1.3 μm, duty ratio as 0.75, grating depth as 0.4 \mu m.