The formation mechanism for the icosahedral central structure of the He1+13 cluster is proposed and its total energy curve is calculated by the method of a Modified Arrangement Channel Quantum Mechanics. The energy is the function of separation R between two nuclei at the center and an apex of the icosahedral central structure. The result of the calculation has shown that the curve has a minimal energy -37.5765 (a.u.) at R = 2.70ao. The binding energy of He+13 with respect to He+ + 12He was calculated to be 1.4046 a.u. This means that the cluster of He+13 may be formed in an icosahedral central structure with strong binding energy.