A new image interpolation method is proposed by using the image priors of nonlocal self-similarity and low rank approximation. Here the traditional cubicspline interpolation is conducted to obtain an initial High resolution (HR) image. The nonlocal similar image patches are vectorized to form data matrices with low rank prior, and thus a low rank regularization term is embedded into the reconstruction model. The texture information measured by entropy of the data matrix is extracted and used to achieve adaptive low rank approximation for retaining the latent fine details of image. The Split bregman iteration (SBI) algorithm and weighted Partial singular values thresholding (PSVT) method are adopted to obtain the optimum solution of the reconstruction model. Experimental results demonstrate the effectiveness of the proposed method in improving image quality in terms of Peak signal to noise ratio (PSNR) and/or Structural similarity (SSIM).