Dual energy computed tomography (DECT) has flu-proved capability of differentiating different materials compared to conventional CT. However, due to non-negligible radiation exposure to patients, dose reduction has recently become a critical concern in CT imaging field. Moreover, direct material decomposition techniques such as numerical inversion can yield significantly amplified noise in the basic material images, and this is another common tissue in DECT imaging. In this work, to address the two issues, we present an iterative algorithm. More specifically, the DECT images are reconstructed by minimizing one objective function consisting a data-fidelity term using Alpha-divergence to describe the statistical distribution of the DE sinogram data and a regularization term utilizing redundant information within DECT images. For simplicity, the present algorithm is termed as "AlphaD-aviNLM". To minimize the associative objective function, a modified proximal forward-backward splitting algorithm is proposed. Digital phantom was utilized to validate and evaluate the present AlphaD-aviNLM algorithm. The experimental results characterize the performance of the present AlphaD-aviNLM algorithm.