Magnetic resonance imaging (MRI) method based on deep learning needs large-quantity and high-quality patient-based datasets for pre-training. However, this is a challenge to the clinical applications because it is difficult to obtain a sufficient quantity of patient-based MR datasets due to the limitation of equipment and patient privacy concerns. In this paper, we propose a novel undersampled MRI reconstruction method based on deep learning. This method does not require any pre-training procedures and does not depend on training datasets. The proposed method is inspired by the traditional deep image prior (DIP) framework, and integrates the structure prior and support prior of the target MR image to improve the efficiency of learning. Based on the similarity between the reference image and the target image, the high-resolution reference image obtained in advance is used as the network input, thereby incorporating the structural prior information into network. By taking the coefficient index set of the reference image with large amplitude in the wavelet domain as the known support of the target image, the regularization constraint term is constructed, and the network training is transformed into the optimization process of network parameters. Experimental results show that the proposed method can obtain more accurate reconstructions from undersampled k-space data, and has obvious advantages in preserving tissue features and detailed texture.