We study the problem of attacking video recognition models in the black-box setting, where the model information is unknown and the adversary can only make queries to detect the predicted top-1 class and its probability. Compared with the black-box attack on images, attacking videos is more challenging as the computation cost for searching the adversarial perturbations on a video is much higher due to its high dimensionality. To overcome this challenge, we propose a heuristic black-box attack model that generates adversarial perturbations only on the selected frames and regions. More specifically, a heuristic-based algorithm is proposed to measure the importance of each frame in the video towards generating the adversarial examples. Based on the frames' importance, the proposed algorithm heuristically searches a subset of frames where the generated adversarial example has strong adversarial attack ability while keeps the perturbations lower than the given bound. Besides, to further boost the attack efficiency, we propose to generate the perturbations only on the salient regions of the selected frames. In this way, the generated perturbations are sparse in both temporal and spatial domains. Experimental results of attacking two mainstream video recognition methods on the UCF-101 dataset and the HMDB-51 dataset demonstrate that the proposed heuristic black-box adversarial attack method can significantly reduce the computation cost and lead to more than 28% reduction in query numbers for the untargeted attack on both datasets.