Image interpolation plays a vital role in digital image processing. In order to preserve image texture detail and edge sharpness, a new method of region adaptive image interpolation based on NSCT (nonsubsampled contourlet transform) is proposed. Image is divided into different regions and interpolated by different methods respectively. Firstly, a new type of C\+2 continuous rational function interpolation model is constructed, and the error estimates are given. Secondly, image edge contour information is captured by the NSCT, and the image is divided into edge region and non-edge region adaptively according to a preset threshold. Finally, as for edge region, edge-directed interpolation technique is used to get high resolution image. Similarly, rational function interpolation algorithm is used in non-edge region. The objective image with higher resolution ratio than the input image is obtained by adaptive interpolation. Compared with the classical image interpolation algorithm, the proposed method is highly competitive not only in PSNR (peak signal to noise ratio) and SSIM (structural similarity index) but also in visual effect. Experimental results show that the proposed algorithm not only has lower time complexity, but also can preserve image details, eliminate phenomenon of edge aliasing, and have a high quality of interpolation image.