For the problems of low-resolution and serious effect from noises of infrared images, an approximate sparsity regularized infrared image super-resolution reconstruction algorithm (ASSR) based on K-SVD (Singular Value Decomposition) was proposed. In consideration of the noise effect from infrared images, an approximate sparsity representation model was first established. On the assumption that the low and high resolution image spaces hold a similar manifold, an approximate sparsity regularized K-SVD based dictionary learning method was proposed with approximate sparsity model and K-SVD method to solve the time-consuming problem of existing dictionary training process. Finally, the high-resolution infrared images were recovered by the high-resolution dictionary and the corresponding low-resolution group sparse coefficients. To verify the performance of the algorithm proposed, it was compared with those of the Sparsity Regularized Super-Resolution Reconstruction (SRSR) and Zeyde algorithm. Experimental results show that the proposed method can reduce the noises of infrared images, and can obtain excellent performance in super-resolution reconstruction.