In recent years, small-scale Unmanned Aerial Vehicles (UAVs) have been used in many video surveillance applications, such as vehicle tracking, border control, dangerous object detection, and many others. Anomaly detection can represent a prerequisite of many of these applications thanks to its ability to identify areas and/or objects of interest without knowing them a priori. In this paper, a One-Class Support Vector Machine (OC-SVM) anomaly detector based on customized Haralick textural features for aerial video surveillance at low-altitude is presented. The use of a One-Class SVM, which is notoriously a lightweight and fast classifier, enables the implementation of real-time systems even when these are embedded in low-computational small-scale UAVs. At the same time, the use of textural features allows a vision-based system to detect micro and macro structures of an analyzed surface, thus allowing the identification of small and large anomalies, respectively. The latter aspect plays a key role in aerial video surveillance at low-altitude, i.e., 6 to 15 m, where the detection of common items, e.g., cars, is as important as the detection of little and undefined objects, e.g., Improvised Explosive Devices (IEDs). Experiments obtained on the UAV Mosaicking and Change Detection (UMCD) dataset show the effectiveness of the proposed system in terms of accuracy, precision, recall, and F1-score, where the model achieves a 100% precision, i.e., never misses an anomaly, but at the expense of a reasonable trade-off in its recall, which still manages to reach up to a 71.23% score. Moreover, when compared to classical Haralick textural features, the model obtains significantly higher performances, i.e., ≈20% on all metrics, further demonstrating the approach effectiveness.