Typhoons Morakot (2009) and Mindulle (2004) were two of the rainiest and most damaging typhoons to hit Taiwan on record, where both cases are associated with a strong low-level southwesterly monsoon flow. The moisture-rich southwesterly monsoon flow and the typhoon-induced northwesterly current usually converge on Taiwan’s Central Mountain Range to produce catastrophic rainfall. The two storms are simulated with a cloud-resolving model (CRM) using the pseudo-global-warming (PGW) methodology to assess the fraction of precipitation attributable to long-term climate change. For each storm, two scenarios are simulated and compared—the control run in present-day climate and the sensitivity test in a past environment four decades ago, where the climate-change signal (“deltas”) is computed using global reanalysis data as the difference between 1990–2009 and 1950–1969. Being realistically reproduced by the CRM at a 3-km grid size in the control run, both typhoons progress in the sensitivity test with highly similar evolution to their present-day counterpart, even though the background in the sensitivity run is slightly cooler and drier than the present. Under the current climate, Morakot and Mindulle produce more rainfall by about 5 mm per day within 300–400 km from the center during their lifespan (equal to an increase of ~4–8%) compared to their counterparts in past climates. Such results are in close agreement with previous studies, and the shift in mean daily rainfall is tested as statistically significant at a confidence level of 99.5%. The water budget analysis shows that the increased rainfall from past to present climate is accounted for mainly by the low-level convergence of moisture associated with a more vigorous secondary circulation and a higher precipitable water amount.