This paper proposes a new algorithm for image interpolation via combining bi-quadratic patches based on point sampling and new edge-directed method (PSE). Usually, the traditional methods use the image data to construct fitting surfaces directly. As a result, the accuracy of the interpolation may not be assured. A model is proposed to compute the point-sampling values first, then a bi-quadratic polynomial surface patch is obtained using point samplings. The whole image surface is constructed by combining all the local patches with weighting functions. For the edges and textures, the PSE adopts a new edge-directed approach to obtain the model parameters. Different from the existing edge-directed approaches, the relationships between the inner members of parameters are taken into account. The experiments for testing the efficiency of the new approach show that the interpolated images reproduced have best results in both PSNR measure and the objective visual quality compared with the competed methods.