Since anomaly targets in hyperspectral images (HSIs) with high spatial resolution appear as connected areas instead of single pixels or subpixels, both spatial and spectral information of HSIs can be exploited for a hyperspectal anomaly detection (AD) task. This article proposes a hyperspectral AD method based on Wasserstein distance (WD) and spatial filtering (called AD-WDSF). Based on the assumption that both background and anomaly targets obey the multivariate Gaussian distribution, background and anomaly target distributions are estimated in the local regions of HSIs. Subsequently, the anomaly intensity of test pixels centered in the local regions are determined via measuring the WD between background and anomaly target distributions. Lastly, spatial filters, i.e., guided filter (GF), total variation curvature filter (TVCF), and Maxtree filter, are exploited to further refine detection results. Experimental results conducted on two real hyperspectral data sets demonstrate that the proposed method achieves competitive detection performance compared with the state-of-the-art AD methods.