A novel 3-D terrain matching algorithm is presented for a passive aircraft navigation system. Stereo matching of a pair of overlapping images can yield a recovered digital elevation model (DEM), which can be matched to the airborne reference DEM of the 3-D terrain. The two DEMs can be represented by the compact representation of contour maps, so the terrain matching is converted to contour-map matching. A contour-map matching algorithm using a combination of Fourier transform and polar transform is then proposed to estimate the associated translation and rotation parameters, which provide the desired position and orientation of the aircraft. Experimental results with real terrain data demonstrate that the proposed algorithm is insensitive to large noise and distortion compared to the previous state of the art, and also has the merits of high reliability and accuracy.