A new approach to image interpolation is proposed. Different from the conventional scheme, the interpolation of a digital image is achieved with a sub-unity coordinate shift technique. In the approach, the original image is first shifted by sub-unity distances matching the locations where the image values need to be restored. The original and the shifted images are then interspersed together, yielding an interpolated image. High quality sub-unity image shift which is crucial to the approach is accomplished by implementing the shift theorem of Fourier transformation. It is well known that under the Nyquist sampling criterion, the most accurate image interpolation can be achieved with the interpolating function (sinc function). A major drawback is its computation efficiency. The present approach can achieve an interpolation quality as good as that with the sinc function since the sub-unity shift in Fourier domain is equivalent to shifting the sinc function in spatial domain, while the efficiency, thanks to the fast Fourier transform, is very much improved. In comparison to the conventional interpolation techniques such as linear or cubic B-spline interpolation, the interpolation accuracy is significantly enhanced. In order to compensate for the under-sampling effects in the interpolation of 3D medical images owing to a larger inter-slice distance, proper window functions were recommended. The application of the approach to 2- and 3-D CT and MRI images produced satisfactory interpolation results.