We report a novel feature-matching method for side-scan sonar images. The method uses nonlinear diffusion filtering to build a nonlinear scale space. The noise-reduction performance is enhanced via nonlinear diffusion filtering, and the improved Perona–Malik diffusion equation results in a more distinct edge and line texture in the side-scan sonar image. The modified feature descriptor reduces the dimensionality of the feature vector so that the computational expense is reduced. Experimental results show that the method provides improved noise-reduction performance and better accuracy than SIFT, SURF, and other state-of-the-art feature-matching algorithms.