Extreme mass ratio inspirals (EMRIs) are key observational targets for future space-based gravitational wave detectors and hold significant value in cosmological research. As a type of “standard siren,” EMRIs offer an independent method to measure the Hubble constant, providing new hope for resolving the “Hubble tension” problem. However, when using the dark siren method combined with galaxy catalogs to statistically infer redshifts, EMRI events occurring in low-luminosity galaxies may not be fully recorded in the galaxy catalogs, leading to potential true hosts being missed. To address this, we propose using galaxy cluster catalogs, which contain numerous member galaxies, including faint ones, effectively reducing the risk of missing true hosts. In this study, we randomly injected three EMRI events and simulated a 2 yr observation of these events using both Laser Interferometric Space Antenna (LISA) and the joint LISA–Taiji network to demonstrate the improvements brought about by incorporating galaxy cluster catalogs into the dark siren methodology. For these three cases, compared to using galaxy catalogs alone, incorporating galaxy cluster catalogs enhanced the measurement precision of the Hubble constant to varying degrees, with a maximum improvement of approximately 41.00%. These results indicate that employing galaxy cluster catalogs in EMRI-based dark siren analyses can more effectively constrain the Hubble constant H₀.