Firefox OS, a new Web-based OS developed by Mozilla mainly for mobile platforms, is designed to realize the 'Boot to the Web' concept for the open Web. It supports users booting to the network directly, launching remote applications and accessing remote data with the standard Web technologies. Although Firefox OS has adopted several mechanisms to enhance its security, its current design is lack of a mechanism to detect 1) applications calling Web API with unusual frequency, and 2) applications consuming abnormal amount of resources. In this paper, we propose an anomaly detection module which takes the system resource usage and the amount of inter-process communication as the inputs to detect whether the system has an anomaly. We also conduct several experiments to examine the ability of the proposed module. The results show that detection accuracy of our module is 0% in false negative rate and 12.5% in false positive rate.