Sparse unmixing has been proven to be an effective hyperspectral unmixing method. The row-sparsity model (using l_2,0 norm to control the sparsity) has outperformed single-sparsity unmixing methods in many scenarios. However, to avoid the NP-hard problem, most algorithms adopt a convex relaxation strategy to solve the l_2,0 norm at the expense of unmixing accuracy and sparsity. In addition, the row-sparsity model might cause aliasing artifacts on the boundaries. To solve these problems, a novel algorithm called two-step iterative row-sparsity hyperspectral unmixing via a low-rank constraint (TRSUnLR) is proposed. TRSUnLR introduces a row-hard-threshold function to solve the l_2,0 norm directly. The low-rank constraint, which can make full use of the global structure of data, is imposed to alleviate the aliasing artifacts. The reweighting strategy is used to further enhance the sparsity. Then we adopt the two-step iterative method under the alternating direction method of multipliers framework to solve the proposed algorithm. Specifically, the current solution is computed by a linear combination of the solutions of two previous iterations. Simulated and real data experiments have proven that the proposed algorithm can obtain better unmixing results.