Deep neural networks (DNNs) for image classification are known to be susceptible to many diversified universal adversarial perturbations (UAPs), where each UAP successfully attacks a large but substantially different set of images. Properly combining the diversified UAPs can significantly improve the attack effectiveness, as the sets of images successfully attacked by different UAPs are complementary to each other. In this paper, we study this novel type of attack by developing a cocktail universal adversarial attack framework. The key idea is to train a set of diversified UAPs and a selection neural network at the same time, such that the selection neural network can choose the most effective UAP when attacking a new target image. Due to the simplicity and effectiveness of the cocktail attack framework, it can be generally used to significantly boost the attack effectiveness of many classic single-UAP methods that use a single UAP to attack all target images. The proposed cocktail attack framework is also able to perform real-time attacks as it does not require additional training or fine-tuning when attacking new target images. Extensive experiments demonstrate the outstanding performance of cocktail attacks.