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Global climate models are good tools for simulating transnational and interregional transport of pollutants such as PM _2.5 , which is of growing interest and importance, for example in human health and socio-economic development studies. However, reliable estimates of PM _2.5 are very challenging for such relatively coarse and simplified models, and even state of the art models fare poorly in matching satellite observations in many highly polluted, and some almost pristine environments. This work describes a novel bias correction method based on multiple linear regression (MLR) modelling. The target data we aim for is global satellite-based data and the PM _2.5 precursors simulated by the Community Earth System Model Version 1.2.2. The statistical method greatly reduced the simulation biases of PM _2.5 worldwide compared with satellite-derived PM _2.5 , especially in highly-polluted regions, such as northern China, the Indo-Gangetic plains, the Democratic Republic of Congo and northwestern Brazil. Root-mean-square differences (RMSD) between continental-averaged observations and simulations are reduced from 75% to 9%. The ensemble RMSD for 13 countries exemplified here is reduced from 116% to 3%. One virtue of the MLR method is that details of the classification of internal mixed modes of each aerosol and their spatial differences are not required. The MLR coefficients are designed to be highly aerosol- and country-dependent, so they provide new perspectives of relative importance of each aerosol to local PM _2.5 and offer clues on observational and simulation biases. The bias-correction method is easily applied for air pollutants simulated by global climate models due to its low computational cost.