With the widespread use of Internet of Things (IoT) devices in recent years, we utilize a variety of hardware devices in our daily life. On the other hand, hardware security issues are emerging. Power analysis is one of the methods to detect anomalous behaviors, but it is hard to apply it to IoT devices where an operating system and various software programs are running. In this paper, we propose an anomalous behavior detection method for an IoT device by extracting application-specific power behaviors. First, we measure power consumption of an IoT device, and obtain the power waveform. Next, we extract an application-specific power waveform by eliminating a steady factor from the obtained power waveform. Finally, we extract feature values from the application-specific power waveform and detect an anomalous behavior by utilizing the local outlier factor (LOF) method. We conduct two experiments to show how our proposed method works: one runs three application programs and an anomalous application program randomly and the other runs three application programs in series and an anomalous application program very rarely. Application programs on both experiments are implemented on a single board computer. The experimental results demonstrate that the proposed method successfully detects anomalous behaviors by extracting application-specific power behaviors, while the existing approaches cannot.