For the problem of low-resolution of infrared nephogram, a method of infrared nephogram super-resolution using coupled over-completed dictionary learning is presented. Based on the analysis of infrared nephogram degradation model, a super-resolution reconstruction framework is built with the sparse representation theory. First, consist a training sample by random sampling a large number of high-resolution and low-resolution sample nephogram patches. Then, construct a couple of dictionaries Dh and Dl by dictionary training, to ensure that the corresponding high-resolution and low-resolution nephogram patches have a similar sparse representation on their dictionaries. We propose a coupled dictionary training method to change the strategy of dictionary update, and the coupled dictionaries were obtained by alternatively optimizing the Dh and Dl in each step of iterative. Finally, for the inputting low-resolution infrared nephogram, Optimized Orthogonal Matching Pursuit (OOMP) algorithm is used to achieve the high-resolution infrared nephogram which satisfies the reconstruction constraint. Numerous experiments show that the proposed algorithm can get a higher quality reconstructed infrared nephogram. Moreover, the algorithm efficiency is more effective than the other dictionary-learning algorithms.