Abstract Typhoon Hagupit (2020), which formed unexpectedly close to land, posed great challenges for forecasters. During its genesis, there was a westward-moving upper-tropospheric cold low (UTCL) to its north. This study investigated the impact of this UTCL on the genesis process using numerical simulations. In the semi-idealized experiment with this UTCL removed (run-Rcold), pre-Hagupit develops faster, but its track drifts southward in the later stage compared with the control experiment (run-cnl). In the experiment with enhanced UTCL (run-Ecold), the simulated track is similar to that in run-cnl, but pre-Hagupit does not develop into a tropical storm. In run-cnl and run-Ecold, the environmental vertical wind shear is larger than that in run-Rcold in the first 2 days, and the simulated pre-Hagupit experiences two prominent dry-air intrusions in the middle and upper troposphere. At the second intrusion, when the weakened UTCL has moved within 2° of pre-Hagupit, the convection in both experiments decays significantly, and the development of the midlevel vortex begins to lag behind that in run-Rcold, and so does the vertical alignment of the low- and midlevel vortices. The UTCL influences the movement of pre-Hagupit by modifying the large-scale steering flows, especially those above 600 hPa. In run-Rcold, due to the absence of the northward component of wind fields related to the UTCL circulation, pre-Hagupit starts to move west-northwestward instead of northwestward as in run-cnl and run-Ecold. Significance Statement Typhoon Hagupit (2020) got named near the 24-h warning line of China. TCs crossing this line are considered to have a significant impact on China within 24 h, or may make landfall within 24 h. After formation, Hagupit rapidly intensified to its peak intensity of 42 m s−1 in 48 h, and made landfall in Zhejiang Province at severe typhoon strength after another 8 h. Both the unexpected genesis and the rapid intensification of Hagupit posed great challenges for forecasters and deserve further investigation. This study focused on the genesis process. We noticed that there was a westward-moving upper-tropospheric cold low (UTCL) in the north during the formation of Hagupit. We have conducted three numerical experiments to investigate the impact of this UTCL on the genesis of Hagupit, and found that the UTCL is an important factor affecting the genesis process. It is detrimental to the vortex development. If the UTCL is removed, Hagupit will develop into a tropical storm more quickly, but its potential landfall point of Hagupit will shift from the southeast coast of China to the Philippines.