The third-generation ground-based gravitational-wave (GW) detector, Cosmic Explorer (CE), is scheduled to start its observation in the 2030s. In this paper, we make a forecast for cosmological parameter estimation with gravitational-wave standard siren observation from the CE. We use the simulated GW standard siren data of CE to constrain the $Lambda$CDM, $w$CDM and CPL models. We combine the simulated GW data with the current cosmological electromagnetic observations including the latest cosmic microwave background anisotropies data from Planck, the optical baryon acoustic oscillation measurements, and the type Ia supernovae observation (Pantheon compilation) to do the analysis. We find that the future standard siren observation from CE will improve the cosmological parameter estimation to a great extent, since the future GW standard siren data can well break the degeneracies generated by the optical observations between various cosmological parameters. We also find that the CEs constraining capability on the cosmological parameters is slightly better than that of the same-type GW detector, the Einstein Telescope. In addition, the synergy between the GW standard siren observation from CE and the 21 cm emission observation from SKA is also discussed.
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