In order to keep the regularity of edges or contour in the magnification of infrared image, an infrared image interpolation algorithm using Aliasing-free Contourlet Transform (AFCT) is proposed. Firstly, Aliasing-free Pyramidal Filter Banks (AFPFB) is combined with Directional Filer Banks (DFB) to construct AFCT. Then, a simple wavelet-based linear interpolation result is used as the initial estimate of the magnified image and fed in an iterative process. In the each iteration, the estimation of the interpolated image is viewed as a noisy version of the ideal high-resolution image and imposing AFCT to it. Subsequently, the denoising process is implemented via the sparsity constraint of the AFCT coefficients. Finally, the magnified infrared image is obtained after several iterations. Experiments show that for the test images, the iterative processing improves the Peak Signal to Noise Ratio (PSNR) with an average 0.837 dB. Moreover, the proposed algorithm obviously outperforms traditional methods based on bilinear interpolation or wavelet in terms of visual quality.