X-ray Computed Tomography (CT) is a powerful nondestructive evaluation (NDE) tool to characterize internal defects and flaws, regardless of surface conditions and sample materials. After data acquisition from a series of X-ray 2D projection imaging, reconstruction methods play a key role to convert raw data (2D radiography) to 3D models. For the past 50 years, standard reconstruction have been performed using analytical methods based on filtered back-projection (FBP) concepts. Numerous iterative methods that have been developed have shown some improvements on certain aspects of the reconstruction quality, but have not been widely adopted due to their high computational requirements. With modern high performance computing (HPC) and graphics processing unit (GPU) technologies, the computing power barrier for iterative methods have been reduced. Iterative methods have more potential to incorporate physical models and a priori knowledge to correct artifacts generated from analytical methods. In this work, we propose a generalized framework for iterative reconstruction with GPU acceleration, which can be adapted for different physical and statistical models in the inner iteration during reconstruction. The forward projection algorithm is an important part of the framework, and is analogous to the ray casting depth map algorithm that was implemented in an earlier work [I] and accelerated using the GPU. Within this framework, different sub-models could be developed in future to deal with different artifacts, such as beam hardening effect and limited angle data problem.