A point descriptor was proposed based on the spectral graph wavelet transform (SGWT) for the pointwise three-dimensional shape matching. SGWT was performed for a series of impulse functions centered at each point on the shape. Since these wavelet coefficients can reflect sufficient multiscale geometric information around each point, they are orderly treated as elements of a high?dimensional vector. Such vector is the descriptor for each point and the geometric disparity between points can be measured by their Euclidean distance. The spectral graph wavelet (SGW) both use low-pass and band-pass filters to analyze the signals and can stably reconstruct them, which makes the proposed descriptor be significant discriminative, compact and robust. The experimental results show that the proposed descriptor can achieve better performance than similar methods.