Hyperspectral sparse unmixing is a task to estimate the optimal fraction (abundance) of materials contained in mixed pixels (endmembers) of a hyperspectral scene, by considering the abundance sparsity. The abundance has a unique property, i.e., high spatial correlation in local regions. This is due to the fact that the endmembers existing in the region are highly correlated. It implies the low rankness of the abundance in the term of endmember. Coming from this prior knowledge, it is expected that considering the low-rank local abundance to the sparse unmixing problem improves the estimation performance. In this paper, we exploit the low-rank local abundance by applying the weighted nuclear norm to the abundance matrix for spatially and spectrally local regions, and add it to the conventional method. We conduct experiments assuming either pure pixels exist on the data or not. The experiment shows that our method yields competitive results and improves the conventional method.