A number of technologically advanced devices, such as radars and satellites, are used in an actual weather forecasting process. Among these devices, the radar is essential equipment in this process because it has a wide observation area and fine resolution in both the time and the space domains. However, the radar can also observe unwanted nonweather phenomena. Anomalous propagation echo is one of the representative nonprecipitation echoes generated by an abnormal refraction phenomenon of a radar beam. Abnormal refraction occurs when the temperature and the humidity change dramatically. In such a case, the radar recognizes either the ground or the sea surface as an atmospheric object. This false observation decreases the accuracy of both quantitative precipitation estimation and weather forecasting. Therefore, a system that can automatically recognize an anomalous propagation echo from the radar data needs to be developed. In this paper, we propose a classification method for separating anomalous propagation echoes from the rest of the weather data by using a combination of a support vector machine classifier and the synthetic minority oversampling technique, to solve the problem of imbalanced data. By using actual cases of anomalous propagation we have confirmed that the proposed method provides good classification results.