A new method in the fault tree analysis (FTA) for the reliability calculation is suggested. Two steps are necessary in traditional method in evaluation of the occurrence probability of top event in fault tree (FT). The first step is to find the minimal outsets, and the second one is to substitute the result into the poincare equation. In order to reduce the enormous computing time of this method, lots of rapid algorithms have been developed. Almost of all achievements were, however, based on the partial structural properties of FT. In this paper, the FT is transformed to a non-linear graph G which has the same minimal outsets of original n, and then the reliability is calculated using the domination theory. In this new method, the required number of equation terms are at most $2^n$ (n is node number of graph G), while $2^m$-1 (m is the number of minimal cutsets) calculation terms are required in the poincare equation in traditional method. Since m>>n in general. our new method reduces the calculation time significantly.