Algebraic Reconstruction Technique (ART) is a widely employed method in computed tomography since it has certain advantages, such as allowing reconstruction of data with missing projections in some angle ranges, over other techniques such as Filtered Back Projection (FBP). Recently, a regularisation technique for ART, RegART, was introduced which provides greatly reduced noise levels. However, a serious drawback of both ART and RegART is the computational complexity of the methods. In this paper, we present a fast version of RegART, which makes use of nVidia's CUDA technology, and show that this approach performs favourably compared to FBP.