The I-V characteristics and spectral response of 4H-SiC metal-semiconductor-metal (MSM) ultraviolet (UV) photodetector have been simulated by MEDICI. The influence of the finger width and spacing of contact electrodes and epitaxial layer thickness on the spectral response has also been analyzed. The results show that the density of dark current is about 10-13 A/μm and the photo-to-dark current ratio is at least 102 at different bias voltages. The range of spectral response is 200～400 nm and the peak responsivity lies in 347 nm. We have also found that the responsivity is increases with the increase of finger width or decrease of finger spacing. The epitaxial layer thickness has almost no effect on responsivity when wavelengh is less than peak wavelength, and the responsivity increases with the increase of epitaxial layer thickness when wavelengh is greater than peak wavelength.