The detection of anomalous Internet-of-Things (IoT) sensor data is extremely important in many industrial applications due to the catastrophic consequences of the faulty or unreliable sensor data. Good anomalous data detection performance with high detection efficiency is indeed a dilemma since it is difficult to derive an explicit detection function to characterize the relationships between the anomalous values and the detection indicator. To overcome this difficulty, the location information of the IoT sensors is exploited in this study to characterize and reconstruct the relationships among the sensor data based on a second-order nonlinear polynomial graph filter (NPGF). The analysis of the sensor data reconstruction model is then conducted in the frequency domain based on the 2-D inverse graph Fourier transform (GFT), and the reconstruction error function for the sensor data is analytically derived based on the second-order GFT coefficients. It is shown that the detection efficiency can be greatly improved if the input graph signal is designed to be bandlimited. The anomalous sensor data detection is then conducted in the frequency domain as high-frequency components are more sensitive to the deviation values. An NPGF-based frequency-domain algorithm is proposed for the anomalous sensor data detection, which is illustrated and validated with a real-world data set for temperature monitoring. The simulation results demonstrate the detection performance and efficiency improvement of the proposed algorithm in anomaly detection.