How to reduce the radiation dose delivered to the patients has always been a important concern since the introduction of computed tomography (CT). Though clinically desired, low-dose CT images can be severely degraded by the excessive quantum noise under extremely low X-ray dose circumstances. Bayesian statistical reconstructions outperform the traditional filtered back-projection (FBP) reconstructions by accurately expressing the system models of physical effects and the statistical character of the measurement data. This work aims to improve the image quality of low-dose CT images using a novel AW nonlocal (adaptive-weighting nonlocal) prior statistical reconstruction approach. Compared to traditional local priors, the proposed prior can adaptively and selectively exploit the global image information. It imposes an effective resolution-preserving and noise-removing regularization for reconstructions. Experimentation validates that the reconstructions using the proposed prior have excellent performance for X-ray CT with low-dose scans.