Removing redundant parameters and computations before the model training has attracted a great interest as it can effectively reduce the storage space of the model, speed up the training and inference of the model, and save energy consumption during the running of the model. In addition, the simplification of deep neural network models can enable high-performance network models to be deployed to resource-constrained edge devices, thus promoting the development of the intelligent world. However, current pruning at initialization methods exhibit poor performance at extreme sparsity. In order to improve the performance of the model under extreme sparsity, this paper proposes a dual-grained lightweight strategy-TEDEPR. This is the first time that TEDEPR has used tensor theory in the pruning at initialization method to optimize the structure of a sparse sub-network model and improve its performance. Specifically, firstly, at the coarse-grained level, we represent the weight matrix or weight tensor of the model as a low-rank tensor decomposition form and use multi-step chain operations to enhance the feature extraction capability of the base module to construct a low-rank compact network model. Secondly, unimportant weights are pruned at a fine-grained level based on the trainability of the weights in the low-rank model before the training of the model, resulting in the final compressed model. To evaluate the superiority of TEDEPR, we conducted extensive experiments on MNIST, UCF11, CIFAR-10, CIFAR-100, Tiny-ImageNet and ImageNet datasets with LeNet, LSTM, VGGNet, ResNet and Transformer architectures, and compared with state-of-the-art methods. The experimental results show that TEDEPR has higher accuracy, faster training and inference, and less storage space than other pruning at initialization methods under extreme sparsity.