The description of local surface features is a critical step in surface matching and object recognition. We present a descriptor for three-dimensional shapes based on the bispectrum of spherical harmonics (BSH). First, points in a support region of a feature point are used to construct a local reference frame, and a histogram is formed by accumulating the points falling within each bin in the support region. Second, spherical harmonic coefficients of the histogram and its bispectrum are calculated. Finally, the feature descriptor is obtained via principal component analysis. We tested our BSH descriptor on public datasets and compared its performance with that of several existing methods. The results of our experiments show that the proposed descriptor outperforms other methods under various noise levels and mesh resolutions.