The perfect matchings counting problem of graphs has important applications in combinatorial optimization, statistical physics, quantum chemistry and other fields. A perfect matching of a graph G is a set of non-adjacent edges that covers all vertices of G . The number of perfect matchings of a graph is closely related to its number of vertices. A fullerene graph   is a 3-connected cubic planar graphs all of whose faces are pentagons and hexagons. Došlić obtained that a fullerene graph with P  vertices has at least P/2+1  perfect matchings, Zhang et al. proved a better lower bound  3(p+2)/4 of the number of perfect matchings of a fullerene graph. We have known that the fullerene graph has a nontrivial cyclic 5-edge-cut if and only if it is isomorphic to the graph T_n for some integer n >=1, where T_n  is the tubular fullerene graph T_n comprised of two caps formed of six pentagons joined by n concentric layers of hexagons.  In this paper, the perfect matchings of the graph T_n  is classified by matching a certain vertex, and recursive relations of a set of perfect matching numbers are obtained. Then the calculation formula of the number of perfect matchings of the graph T_n  is given by recursive relationships. Finally, we get the number of perfect matchings of  T_n  with P  vertices.