The current-voltage (I-V) characteristics of 4H-SiC metal-semiconductor-metal (MSM) ultraviolet photodetector with different finger widths and spacings, different carrier concentrations and thicknesses of n-type epitaxial layer are simulated. The simulation results indicate that the dark current and the photocurrent both increase when the finger width increases. But the effect of finger width on the dark current is more significant. On the other hand, the effect of finger spacing on the photocurrent is more significant. When the finger spacing increases, the photocurrent decreases and the dark current is almost changeless. In addition, it is found that the smaller the carrier concentration of n-type epitaxial layer is, the smaller the dark current and the larger the photocurrent will be. It is also found that I-V characteristics of MSM detector also depend on the epitaxial layer thickness. The dark current of detector is smaller and the photocurrent is larger when the epitaxial layer thickness is about 3 \mum.