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Introduction: The Multi-Channel Imager (MCI), one of the back-end modules of the future China Space Station Telescope (CSST), is designed for high-precision space-based astronomical observations. This paper evaluates the astrometric capability of the MCI based on simulated observational images and Gaia data: the M31 galaxy is selected as a representative case to validate the astrometric capability by calculating the proper motions (PMs) of the M31 member stars. Method: We analyze the stellar centroids of the simulated images in the R, I and G bands, positional uncertainty of 2.5 mas for brighter foreground reference stars from the Gaia DR3 catalog and of 7.5 mas for the fainter M31 member stars, are adopted respectively. The theoretical PMs are generated from the adopted velocity field model, rotation curve, and stellar surface density profile. And the simulated observed PMs are generated from the aforementioned position uncertainties and theoretical PMs. Result: We conclude that the precision of the MCI derived PMs strongly depends on the number of astrometric epochs per year. Specifically, uncertainty of 10 μas/yr is achievable with 10 epochs per year, and of 5 μas/yr with 50 epochs ignoring possible systematic effects. And symmetrically distributed observed fields yield better M31 kinematic parameters. Discussion: Unknown systematic errors, space environment effects on detectors, dithering strategies, and observation schedules can affect the PMs of M31, the above issues need further analysis and validation in future work. [ABSTRACT FROM AUTHOR]