This paper proposes a spatial filter design for surface sound source separation (SSS), which is called the scan-and-sum beamformer. It performs SSS of surface sources distributed in the azimuth angle domain. A sound source is mainly modeled as a point source in signal processing technology, though surface sources with a certain shape and size are common in the real world. The basic idea is to decompose a surface source into point sources distributed within a region, and then integrate results from point source sub-beamformers. Simulations show that the proposed method improves signal-to-interference ratio for a mixture of three surface sources.