Recently, deep learning techniques have been used for low-dose CT (LDCT) reconstruction to reduce the radiation risk for patients. Despite the improvement in performance, the network models used for LDCT reconstruction are becoming increasingly complex and computationally expensive under the mantra of “deeper is better”. However, in clinical settings, lightweight models with a low computational cost and short reconstruction times are more popular. For this reason, this paper proposes a computationally efficient CNN model with a simple structure for sparse-view LDCT reconstruction. Inspired by super-resolution networks for natural images, the proposed model interpolates projection data directly in the sinogram domain with a fully convolutional neural network that consists of only four convolution layers. The proposed model can be used directly for sparse-view CT reconstruction by concatenating the classic filtered back-projection (FBP) module, or it can be incorporated into existing dual-domain reconstruction frameworks as a generic sinogram domain module. The proposed model is validated on both the 2016 NIH-AAPM-Mayo Clinic LDCT Grand Challenge dataset and The Lung Image Database Consortium dataset. It is shown that despite the computational simplicity of the proposed model, its reconstruction performance at lower sparsity levels (1/2 and 1/4 radiation dose) is comparable to that of the sophisticated baseline models and shows some advantages at higher sparsity levels (1/8 and 1/15 radiation dose). Compared to existing sinogram domain baseline models, the proposed model is computationally efficient and easy to train on small training datasets, and is thus well suited for clinical real-time reconstruction tasks.