In this research, we propose a 3D volume reconstruction method using x-ray images and present a series of calibration methods to implement it in an x-ray imaging system. In our previous work, we have proposed an advanced 3D reconstruction algorithm based on algebraic reconstruction technique(ART), called a uniform and simultaneous ART(USART). In practice, however, there are two main issues to implement it in a realized x-ray imaging system. The first one is huge computation time and memory required in achieving 3D volume, which is a common limitation in ART methods. The second issue is the problem on system calibration for determining the geometry of the x-ray imaging conditions which are necessary information in ART method. This work addresses solving out these problems : We propose a fast computing model of USART, where spherical voxel elements are employed in computation to reduce computation time and memory. And a calibration method is proposed here to identify the x-ray imaging geometry based on a cone beam projection model. For this purpose, a reference grid pattern is locally displaced to predetermined positions, and then their relative coordinates are determined by analyzing the image variations according to the displacements of the grid pattern. The validity of the proposed 3D reconstruction method is investigated from a series of experiments.