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This paper introduces a new sparsity prior to the estimation of dense flow fields. Based on this new prior, a complex flow field with motion discontinuities can be accurately estimated by finding the sparsest representation of the flow field in certain domains. In addition, a stronger additional sparsity constraint on the flow gradients is incorporated into the model to cope with the measurement noises. Robust estimation techniques are also employed to identify the outliers and to refine the results. This new sparsity model can accurately and reliably estimate the entire dense flow field from a small portion of measurements when other measurements are corrupted by noise. Experiments show that our method significantly outperforms traditional methods that are based on global or piecewise smoothness priors.