Conventional sparse coding based super-resolution (SR) methods obtained promising performance by learning overcomplete dictionaries for low-resolution (LR) and high-resolution (HR) feature spaces, and assuming that the sparse representation of a HR feature vector was identical or linear to the sparse representation of the corresponding LR one. However, in fact, the relationship between LR and HR sparse domains is nonlinear due to the complicated degradation of the observed image. To learn the relation more precisely, an assumption called “the same-support constraint” is adopted in our proposed method, which forces LR/HR image patches to activate the atoms lying in the same locations of the LR/HR dictionaries. Under the same-support constraint, our approach first learns LR dictionary, and then obtains HR dictionary and a nonlinear mapping between LR/HR sparse domains by training them iteratively. LR/HR dictionaries learned individually can explore structural characteristics of their corresponding feature spaces well, while the mapping learned iteratively can reveals accurately the intrinsic non-linear relationship between LR and HR sparse domains. Experimental results show that the proposed method outperforms the compared sparse learning based single image super-resolution methods.