The essential problem for computered tomography (CT) is to reconstruct a function (an image) from a finite set of its Radon projections. We propose a reconstruction algorithm, called OPED, based on the Orthogonal Polynomial Expansion on the Disk. The algorithm works naturally with the fan data and can be implemented efficiently. Furthermore, it is proved that the algorithm converges uniformly under a mild condition on the function. Numerical experiments have shown that the method is fast, stable, and has a small global error.