As a completely independent method, the measurement of time delay of strongly lensed quasars (TDSL) are crucial to resolve the Hubble tension. Extensive monitoring is required but so far limited to a small sample of strongly lensed quasars. Together with several partner institutes, Beijing Normal University is constructing a 1.93 m reflector telescope at the Muztagh-Ata site in west China, which has the world class observing conditions with median seeing of 0."82 and median sky brightness of 21.74 \(\rm mag arcsec^{-2}\) in V-band during the dark time. The telescope will be equipped with both a three-channel imager/photometer which covers 3500–11,000 Å wavelength band, and a low-medium resolution (λ/δλ = 500/2000/7500) spectrograph. In this paper, we investigate the capability of the Muztagh-Ata 1.93 m telescope in measuring time delays of strongly lensed quasars. We generate mock strongly lensed quasar systems and light curves with microlensing effects based on five known strongly lensed quasars, i.e., RX J1131-1231, HE 0435-1223, PG 1115+080, WFI 2033-4723 and SDSS 1206+4332. In particular, RX J1131-1231 is generated based on the lens modeling results of Suyu et al. Due to the lack of enough information, the other four systems are calculated by a simple analytical approximation. According to simulations, for RX J1131-like systems (wide variation in time delay between images) the TDSL measurement can be achieved with the precision about Δt = 0.5 day with four seasons campaign length and 1 day cadence. This accuracy is comparable to the up-coming TDCOSMO project. And it would be better when the campaign length keeps longer and with high cadence. As a result, the capability of the Muztagh-Ata 1.93 m telescope allows it to join the network of TDSL observatories. It will enrich the database for strongly lensed quasar observations and make more precise measurements of time delays, especially considering the unique coordinate of the site.