The dynamic downscaling dataset provides useful insight for future climate change at the local scale. The original downscaled dataset, however, inevitably involves bias and hampers its further applications. This study presents a bias correction method that uses the quantile mapping method to a dynamic downscaled dataset originated from the Meteorological Research Institute (MRI). Daily solar radiation and hourly typhoon rainfall are selected as target variables to be corrected because they are critical variables in hydrological and agricultural practice. The results reveal that the original biases in the two datasets were markedly reduced and the statistical characteristics in the projections were much closer to that in the observations. After correction, the future changes in daily solar radiation and hourly typhoon rainfall are also evaluated. A decrease in solar radiation is suggested up to ~5% in south and west parts of Taiwan in the late 21^st century while an increasing amount, about 2%, will occur in the mountain areas. A significant increase in typhoon rainfall amount, up to ~50% is observed in the west and central parts of Taiwan in the late 21^st century and ~20% in the early 21^st century (2015 - 2039). A decrease in typhoon rainfall amount, up to ~-30%, is clear for the north and east parts of Taiwan.