This paper describes an iterative algorithm, MENT, which produces a maximum entropy solution to the problem of reconstructing a source from a discrete set of projection data. Whereas the MART algorithm considered by Lent in (“1976 Society of Photographic Scientists and Engineers Conference Proceedings,” SPSE, Washington, D.C., 1977) uses a rectangular grid to represent the source, MENT uses a discretization which is better suited to the problem. Unlike MART, MENT does not require the evaluation of logarithms or exponentials. The storage requirements are also lower for MENT. Numerical examples are given of a two-dimensional reconstruction from five views. MENT and MART are compared with regard to convergence rates, artifact formation, and stability against noise errors in the data. A three-dimensional version of the algorithm is also considered; we give an example of a direct three-dimensional reconstruction from four views.