Low-dose computed tomography (LDCT) imaging technique attracts intensive attention in the medical community as it can significantly decrease the potential radiation risk to human body. Nevertheless, the imaging quality of LDCT is contaminated by noise that compromises the clinical diagnosis and analysis. In this work, a novel deep unfolding network-based LDCT images denoising method is investigated which combines the high performance of data-driven deep learning methods with the interpretability of model-based traditional methods. The convolutional sparse representation is employed for modeling the whole LDCT image rather than image patches to avoid the boundary artifacts. A U-shape architecture inspired by the U-Net is embedded to get the utmost out of the limited LDCT images and mine multi-resolution features of each image. A learnable iterative shrinkage-thresholding strategy is presented to obtain the sparse map for describing the feature of each resolution. With a compound loss function to conduct the training of the network, the proposed method can efficiently denoise the LDCT images.