In X-ray computed tomography (CT) iterative methods are more suitable for the reconstruction of images with high contrast and precision in noisy conditions and from a small number of projections. However, in practice, these methods are not widely used due to the high computational cost of their implementation. Nowadays technology provides the possibility to reduce effectively this drawback. It is the goal of this work to develop a fast GPU-based algorithm to reconstruct high quality images from under sampled and noisy projection data.