Small unmanned aerial vehicles can be effectively used for aerial video surveillance. Although the field of view of the camera mounted on the drone is limited, flying drones can expand their surveillance coverage. In this paper, we address the detection of moving targets in urban environments with a moving drone. The drone moves at a constant velocity and captures video clips of moving vehicles such as cars, buses, and bicycles. Moving vehicle detection consists of frame registration and subtraction followed by thresholding, morphological operations and false blob reduction. First, two consecutive frames are registered; the coordinates of the next frame are compensated by a displacement vector that minimizes the sum of absolute difference between the two frames. Second, the next compensated frame is subtracted from the current frame, and the binary image is generated by thresholding. Finally, morphological operations and false alarm removal extract the target blobs. In the experiments, the drone flies at a constant speed of 5.1 m/s at an altitude of 150 m while capturing video clips of nine moving targets. The detection and false alarm rates as well as the receiver operating characteristic curves are obtained, and the drone velocities in the x and y directions are estimated by the displacement vector. The average detection rate ranges from 90% to 97% while the false alarm rate ranges from 0.06 to 0.5. The root mean square error of the speed is 0.07 m/s when the reference frame is fixed, showing the robustness of the proposed method.