We deal with the triangular mesh-discontinuous finite element method for solving the time-dependent anisotropic neutron transport problem in two-dimensional cylindrical geometry. A priori estimate of the numerical solution is given. Stability is proved. We have computed a two dimensional anisotropic neutron transport problem and a Tungsten-Carbide critical assembly problem by using the numerical method. In comparision with DSN method and the experiments the method is satisfactory.