In this paper, we propose a deep neural network-based method for estimating speed of vehicles on roads automatically from videos recorded using unmanned aerial vehicle (UAV). The proposed method includes the following; (1) detecting and tracking vehicles by analyzing the videos, (2) calculating the image scales using the distances between lanes on the roads, and (3) estimating the speeds of vehicles on the roads. Our method can automatically measure the speed of the vehicles from the only videos recorded using UAV without additional information in both directions on the roads simultaneously. In our experiments, we evaluate the performance of the proposed method with the visual data at four different locations. The proposed method shows 97.6% recall rate and 94.7% precision rate in detecting vehicles, and it shows error (root mean squared error) of 5.27 km/h in estimating the speeds of vehicles.