A new quantile-based mapping method is developed for the bias correction of monthly global circulation model outputs. Compared to the widely used quantile-based matching method that assumes stationarity and only uses the cumulative distribution functions (CDFs) of the model and observations for the baseline period, the proposed method incorporates and adjusts the model CDF for the projection period on the basis of the difference between the model and observation CDFs for the training (baseline) period. Thus, the method explicitly accounts for distribution changes for a given model between the projection and baseline periods. We demonstrate the use of the new method over northern Eurasia. We fit a four-parameter beta distribution to monthly temperature fields and discuss the sensitivity of the results to the choice of distribution range parameters. For monthly precipitation data, a mixed gamma distribution is used that accounts for the intermittent nature of rainfall. To test the fidelity of the proposed method, we choose 1970–1999 as the baseline training period and then randomly select 30 years from 1901–1999 as the projection test period. The bootstrapping is repeated 30 times to mimic different climate conditions that may occur, and the results suggest that both methods are comparable when applied to the 20th century for both temperature and precipitation for the examined quartiles. We also discuss the dependence of the bias correction results on the choice of time period for training. This indicates that the remaining biases in the bias-corrected time series are directly tied to the model's performance during the training period, and therefore care should be taken when using a particular training time period. When applied to the Intergovernmental Panel on Climate Change fourth assessment report (AR4) A2 climate scenario projection, the data time series after bias correction from both methods exhibit similar spatial patterns. However, over regions where the climate model shows large changes in projected variability, there are discernable differences between the methods. The proposed method is more sensitive to a reduction in variability, exemplified by wintertime temperature. Further synthetic experiments using the lower 33% and upper 33% of the full data set as the validation data suggest that the proposed equidistance quantile-matching method is more efficient in reducing biases than the traditional CDF mapping method for changing climates, especially for the tails of the distribution. This has important consequences for the occurrence and intensity of future projected extreme events such as heat waves, floods, and droughts. As the new method is simple to implement and does not require substantial computational time, it can be used to produce auxiliary ensemble scenarios for various climate impact-oriented applications.