  Gravitational waves (GWs) from compact binary coalescences encode the
absolute luminosity distances of GW sources. Once the redshifts of GW sources
are known, one can use the distance-redshift relation to constrain cosmological
parameters. One way to obtain the redshifts is to localize GW sources by GW
observations and then use galaxy catalogs to determine redshifts from a
statistical analysis of redshift information of the potential host galaxies,
commonly referred to as the dark siren method. The third-generation (3G) GW
detectors are planned to work in the 2030s and will observe numerous compact
binary coalescences. Using these GW events as dark sirens requires high-quality
galaxy catalogs from future sky survey projects. The China Space Station
Telescope (CSST) will be launched in 2024 and will observe billions of galaxies
within a 17500 deg$^2$ survey area with redshift up to $z\sim 4$, providing
photometric and spectroscopic galaxy catalogs. In this work, we simulate the
CSST galaxy catalogs and the 5-year GW data from the 3G GW detectors and
combine them to infer the Hubble constant ($H_0$). Our results show that the
measurement precision of $H_0$ could reach the sub-percent level, meeting the
standard of precision cosmology. We conclude that the synergy between CSST and
the 3G GW detectors is of great significance in measuring the Hubble constant.
