In classical machine learning, a set of weak classifiers can be adaptively combined for improving the overall performance, a technique called adaptive boosting (or AdaBoost). However, constructing a combined classifier for a large data set is typically resource consuming. Here we propose a quantum extension of AdaBoost, demonstrating a quantum algorithm that can output the optimal strong classifier with a quadratic speedup in the number of queries of the weak classifiers. Our results also include a generalization of the standard AdaBoost to the cases where the output of each classifier may be probabilistic. We prove that the query complexity of the non-deterministic classifiers is the same as those of deterministic classifiers, which may be of independent interest to the classical machine-learning community. Additionally, once the optimal classifier is determined by our quantum algorithm, no quantum resources are further required. This fact may lead to applications on near term quantum devices.