Obtaining accurate and reliable images from low-dose computed tomography (CT)\nis challenging. Regression convolutional neural network (CNN) models that are\nlearned from training data are increasingly gaining attention in low-dose CT\nreconstruction. This paper modifies the architecture of an iterative regression\nCNN, BCD-Net, for fast, stable, and accurate low-dose CT reconstruction, and\npresents the convergence property of the modified BCD-Net. Numerical results\nwith phantom data show that applying faster numerical solvers to model-based\nimage reconstruction (MBIR) modules of BCD-Net leads to faster and more\naccurate BCD-Net; BCD-Net significantly improves the reconstruction accuracy,\ncompared to the state-of-the-art MBIR method using learned transforms; BCD-Net\nachieves better image quality, compared to a state-of-the-art iterative NN\narchitecture, ADMM-Net. Numerical results with clinical data show that BCD-Net\ngeneralizes significantly better than a state-of-the-art deep (non-iterative)\nregression NN, FBPConvNet, that lacks MBIR modules.\n