Cone-beam computed tomography (CBCT) plays an important role in radiation therapy. Statistical iterative reconstruction (SIR) algorithms with specially designed penalty terms provide good performance for low-dose CBCT imaging. Among others, the total variation (TV) penalty is the current state-of-the-art in removing noises and preserving edges, but one of its well-known limitations is its staircase effect. Recently, various penalty terms with higher order differential operators were proposed to replace the TV penalty to avoid the staircase effect, at the cost of slightly blurring object edges. We developed a novel SIR algorithm using a neural network for CBCT reconstruction. We used a data-driven method to learn the "potential regularization term" rather than design a penalty term manually. This approach converts the problem of designing a penalty term in the traditional statistical iterative framework to designing and training a suitable neural network for CBCT reconstruction. We proposed using transfer learning to overcome the data deficiency problem and an iterative deblurring approach specially designed for the CBCT iterative reconstruction process during which the noise level and resolution of the reconstructed images may change. Through experiments conducted on two physical phantoms, two simulation digital phantoms, and patient data, we demonstrated the excellent performance of the proposed network-based SIR for CBCT reconstruction, both visually and quantitatively. Our proposed method can overcome the staircase effect, preserve both edges and regions with smooth intensity transition, and provide reconstruction results at high resolution and low noise level.