In this paper, we propose a spectral interpolation method using a distortion geodesic line, which is defined as the curve with minimal accumulated distortion. We apply the distortion geodesic line to interpolation of two given spectra (vectors). The first part of this paper describes the definition of the distortion geodesic line. It is shown that a geodesic line is characterized by the Riemannian metric which is introduced as a bilinear form of the second partial derivatives of a given distortion measure. The second part describes an inequality for the WLR measure on several interpolating curves. This inequality guarantees that the accumulated WLR distortion value for any two given spectra, ƒ(0) and ƒ(1), on the correlation interpolation curve, is always smaller than the direct WLR value dWLR(ƒ(0), ƒ(1)). This property is easily extended to a category of several distortion measures. The third part describes an application of the distortion geodesic line to spectral interpolation, and numerically shows that the interpolation line on the correlation parameter is the best of several kinds of LPC based parameters.