Computed tomography (CT) reconstructs sectional images from X-ray projections acquired from multiple angles around an object. In the case of low-dose or sparse-view scans, the image reconstruction using classical tomographic algorithms can produce severe noise and artifacts. To address this issue, we present a deep learning-based image reconstruction method derived from maximum a posteriori (MAP) estimation. In the Bayesian statistics framework, the gradient of logarithmic probability density distribution of the image, i.e., the score function, plays a crucial role, contributing to the process of image reconstruction. We develop an improved score matching (ISM) solution for the image reconstruction by leveraging Gaussian mixture to characterize noise distributions. The reconstruction algorithm with the score function theoretically guarantees the convergence of the iterative process. Our results also show that this reconstruction method can produce higher quality images compared to state-of-the-art reconstruction methods.