Seismic denoising is an essential step for seismic data processing. Conventionally, dictionary learning (DL) methods for seismic denoising always assume the representation coefficients to be sparse and the dictionary to be normalized or a tight frame. Current DL methods need to update the dictionary and the coefficients in an alternating iterative process. However, the dictionary obtained from the DL method often needs to be recalculated for different input data. Moreover, the performance of DL for seismic noise removal is related to the parameter selection and the prior constraints of dictionary and representation coefficients. Recently, deep learning demonstrates promising performance in data prediction and classification. Following the architecture of DL algorithms strictly, we have developed a novel and interpretable deep unfolding dictionary learning (DUDL) method for seismic denoising by unfolding the iterative algorithm of DL into a deep neural network (DNN). The proposed architecture of DUDL contains two main parts: the first is to update the dictionary and representation coefficients using least-squares inversion and the second is to apply a DNN to learn the prior representation of dictionary and representation coefficients, respectively. Numerical synthetic and field examples find the effectiveness of our method. More importantly, this method for seismic denoising obtains the dictionary for different seismic data adaptively and is suitable for seismic data with different noise levels.