With the widespread use of automated speech recognition (ASR) systems in modern consumer devices, attack against ASR systems have become an attractive topic in recent years. Although related white-box attack methods have achieved remarkable success in fooling neural networks, they rely heavily on obtaining full access to the details of the target models. Due to the lack of prior knowledge of the victim model and the inefficiency in utilizing query results, most of the existing black-box attack methods for ASR systems are query-intensive. In this paper, we propose a new black-box attack called the Monte Carlo gradient sign attack (MGSA) to generate adversarial audio samples with substantially fewer queries. It updates an original sample based on the elements obtained by a Monte Carlo tree search. We attribute its high query efficiency to the effective utilization of the dominant gradient phenomenon, which refers to the fact that only a few elements of each origin sample have significant effect on the output of ASR systems. Extensive experiments are performed to evaluate the efficiency of MGSA and the stealthiness of the generated adversarial examples on the DeepSpeech system. The experimental results show that MGSA achieves 98% and 99% attack success rates on the LibriSpeech and Mozilla Common Voice datasets, respectively. Compared with the state-of-the-art methods, the average number of queries is reduced by 27% and the signal-to-noise ratio is increased by 31%.