The conventional discrete-ordinates method is modified and developed for the analysis of two-dimensional axisymmetric cylindrical enclosure with absorbing, emitting, and either isotropically or anisotropically scattering gray medium. The main characteristic of the present method is that the control angles can be arbitrarily specified pertaining to each problem dealt with. The scattering phase function is approximated by a finite series of Legendre polynomials. In order to validate the formulations, four benchmark problems are considered and their results are compared with other predictions or experimental data. It is shown that the present method is quite accurate, computationally efficient, and easy to use for the analysis of axisymmetric radiation heat transfer.