The image quality in low dose computed tomography (LDCT) can be severely degraded by amplified mottle noise and streak artifacts. Although the iterative reconstruction (IR) algorithms bring sound improvements, their high computation cost remains a major inconvenient. In this work, a deep iterative reconstruction estimation (DIRE) strategy is developed to estimate IR images from LDCT analytic reconstructions images. Within this DIRE strategy, a 3D residual convolutional network (3D ResNet) architecture is proposed. Experiments on several simulated and real datasets as well as comparisons with state-of-the-art methods demonstrate that the proposed approach is effective in providing improved LDCT images.