An efficient implement for Algebraic Reconstruction Technique (ART) is presented in this paper.The coefficient matrix in the original ART is split into radial matrix and the coefficient matrix of the radial.The slope and intercept of each radial are kept in the radial matrix.The coefficient matrix of the radial is calculated before iteration

and considering the correlation of the lines with the same projection angle it can be computed iteratively

with much time saved.The experiments using Shepp-logan phantom show that the results of this method are as good as the traditional one with great reduction of memory.