The detection of moving objects under a free-moving camera is a difficult problem because the camera and object motions are mixed together and the objects are often detected into the separated components. To tackle this problem, we propose a fast moving object detection method using optical flow clustering and Delaunay triangulation as follows. First, we extract the corner feature points using Harris corner detector and compute optical flow vectors at the extracted corner feature points. Second, we cluster the optical flow vectors using K-means clustering method and reject the outlier feature points using Random Sample Consensus algorithm. Third, we classify each cluster into the camera and object motion using its scatteredness of optical flow vectors. Fourth, we compensate the camera motion using the multi-resolution block-based motion propagation method and detect the objects using the background subtraction between the previous frame and the motion compensated current frame. Finally, we merge the separately detected objects using Delaunay triangulation. The experimental results using Carnegie Mellon University database show that the proposed moving object detection method outperforms the existing other methods in terms of detection accuracy and processing time.