According to recent results on Middlebury, MPI Sintel, and KITTI benchmarks, the accuracy of optical flow estimation algorithms has been significantly improved. The speed of them, however, has been too slow to meet the requirement of real-time applications. As a result, some parallel architectures (such as FPGA or GPU) have to be used for accelerating. Therefore, reducing the computational cost of optical flow estimation makes a lot of sense. To overcome the above issues, this paper proposes a fast local method based on 3D-gradients and approximate nearest-neighbor field (NNF), which is different from the widely used global model. In our method, NNF is used to provide initial optical flow field, and the proposed fast 3D-gradients-based local operator is used to propagate flow from coarse level to finer level in the coarse-to-fine refinement. We implement two versions of our method (with/without NNF initialization). Experimental results show that our method has a significant advantage for speed over other methods, where the fast version is capable of processing $Urban$ sequence ( $640\times 480$ ) at $\approx 10$ frames/s without parallel architectures. Meanwhile, our accuracy is also within acceptable levels on both small and large motion for some real-time applications.