The medical magnetic resonance (MR) image reconstruction is one of the key technologies in the field of magnetic resonance imaging (MRI). The compressed sensing (CS) theory indicates that the image can be reconstructed accurately from highly undersampled measurements by using the sparsity of the MR image. However, how to improve the image reconstruction quality by employing more sparse priors of the image becomes a crucial issue for MRI. In this paper, an adaptive image reconstruction model fusing the double dictionary learning is proposed by exploiting sparse priors of the MR image in the image domain and transform domain. The double sparse model which combines synthesis sparse model with sparse transform model is applied to the CS MR image reconstruction according to the complementarity of synthesis sparse and sparse transform model. Making full use of the two sparse priors of the image under the synthesis dictionary and transform dictionary learning, the proposed model is tackled in stages by the iterative alternating minimization algorithm. The solution procedure needs to utilize the synthesis and transform K-singular value decomposition (K-SVD) algorithms. Compared with the existing MRI models, the experimental results show that the proposed model can more efficiently improve the quality of the image reconstruction, and has faster convergence speed and better robustness to noise.