As part of China's first Mars exploration mission 'Tianwen-1', the Zhurong rover has successfully touched down on the surface of southern Utopia Planitia on May 15th 2021 and has been conducting surface operations for several months. A multispectral camera (MSCam), as an important payload onboard the Zhurong rover, aims to acquire multispectral images to investigate the morphological characteristics and mineralogic properties of the Martian surface. In this study, a detailed optimization design for the MSCam was carried out to achieve the abovementioned scientific objectives. The MSCam can perform multispectral imaging without chromatic aberration by utilizing eight narrow bandwidth filters made of glass of different thicknesses. Clear images of observation targets at different distances can be obtained by utilizing the six focal plane compensation lenses of varying thicknesses through the rotation of wheels. Calibration experiments, key specification tests and ground verification tests were also conducted in this study. Our results show that the pixel resolution of the MSCam can reach 0.146 mrad, the system static modulation transfer function (MTF) of the MSCam is better than 0.25@525 nm, and the signal-to-noise ratio (SNR) is higher than 40 dB, all of which allow clear imaging and accurate multispectral data acquisition of the targets. The high-resolution images obtained by the MSCam will provide detailed geological context for the data interpretation of other payloads on the rover, such as the Mars surface composition detector (MarSCoDe). The mineralogy information of the targets (e.g., fresh rock, dune) indicated by the MSCam multispectral data will also help to constrain the surface material composition of Mars.