For the study of climate change, many General Circulation Models (GCM)s have been designed, modeling the climate on the planet Earth slightly differently either by emphasizing predictions in specific regions or by incorporating varied or uniquely modeled parameters. To extract a robust signal from the diverse outputs, models are typically combined into multimodel ensembles. Their results are summarized in various ways, including (possibly weighted) multimodel means, medians and other statistics, within a Bayesian framework or not. In this work, we introduce an new probability aggregation method termed "alpha-pooling" which builds an aggregated Cumulative Probability Function (CPF) designed to be closer to a reference CPF over the calibration period. α-pooling assigns a weight to each CPF, which is an increasing function of its closeness to the reference CPF. Key to the α-pooling is a parameter α that describes the type of aggregation, which includes linear aggregation and log-linear aggregation. We first establish that α-pooling is a proper aggregation method verifying some optimal properties. Then, focusing on climate models over Western Europe, several experiments are run in order to assess the performance of αpooling against methods currently available, including multi-model means and weighted variants. A perfect model experiment and a sensitivity analysis to the set of climate models are run. Our findings demonstrate the superiority of the proposed method, indicating that alpha-pooling presents a robust and efficient way to combine GCM's CPF. The results of this study show that the CDFs pooling strategy for "multi-model bias correction" is a credible alternative to usual GCM-by-GCM correction methods, by allowing to handle and consider several climate models at once.