Abstract: Analytic function expansion nodal method is often used to solve hexagonal geometry reactor problems whose kernel is that the intra-nodal flux distribution is expanded in a series of analytic basic functions for each group. In some cases, this method is not convergence and two stabilization techniques are introduced to resolve the instability problem. One is truncation approximation and the other is Taylor expansion. Compared with the VVER440 benchmark results, both techniques not only ensure the calculation accuracy but also give a good solution for numerical instability problems.