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Bias correction is an essential technique to correct climate model outputs for local or site-specific climate change impact studies. Most commonly used bias correction methods operate on a single variable, which ignores dependency among multiple variables. The misrepresentation of multivariable dependence may result in biased assessment of climate change impacts. To solve this problem, a new multivariate bias correction method referred to as two-stage quantile mapping (TSQM) is proposed by combining a single-variable bias correction method with a distribution-free shuffle approach. Specifically, a quantile mapping method is used to correct the marginal distribution of single variable and then a distribution-free shuffle approach to introduce proper multivariable correlations. The proposed method is compared with the other four state-of-the-art multivariate bias correction methods for correcting monthly precipitation, and maximum and minimum temperatures simulated by global climate models. The results show that the TSQM method is capable of both bias correcting univariate statistics and inducing proper inter-variable rank correlations. Especially, it outperforms all the other four methods in reproducing inter-variable rank correlations and in simulating mean temperature and potential evaporation for wet and dry months of the validation period. Overall, without complex algorithm and iterations, TSQM is fast, simple and easy to implement, and is proved a competitive bias correction technique to be widely applied in climate change impact studies.