Sparse coding method has been used for seismic denoising, as the data can be sparsely represented by the sparse transform and dictionary learning (DL) methods. DL methods have attracted wide attention because the learned dictionary is adaptive. However, for seismic denoising, the dictionary learned from the noise data is a mix of atoms representing seismic data patterns and atoms representing noise patterns. To make the dictionary contain more atoms to represent seismic data, we consider adding to the dictionary the local and nonlocal similarities of the data via the structured graph and propose a new DL method, namely, the structured graph dictionary learning (SGDL). The atoms of dictionary learned by the SGDL are smooth, which implies smoothness of any signal represented over this dictionary. In addition, in the dictionary domain, we use the nonlocal model, namely, SSC-GSM that connects Gaussian scale mixture (GSM) with simultaneous sparse coding (SSC), to represent the seismic data. We apply the method to the synthetic data and two kinds of field data. Results show that our method can better remove strong noise and retain the seismic weak events also.