Image interpolation has been used widely to perform magnification by predicting missing details from a sampled image. As most of the signal information is distributed around edges and areas of sharp changes, there is a need of designing an interpolation technique that is able to predict these changes precisely. However, many conventional polynomial-based interpolation methods tend to smooth or blur out image details around the edges. In this paper, a novel method called Lagrange time delay estimation interpolation (LATDEI) model is proposed, to confront the problem. Simulation results shows that the consistency of LATDEI performance, in obtaining better images, implies that it is a promising estimator for image interpolation of various images. Compared to two traditional methods, the proposed LATDEI method improves the subjective quality of the interpolated edges while providing a better resolution.