We introduce the process of the development in the Nuclear Structure Model, the Quantum Theory of the Projected Shell Model and the improvement of the calculating program. Besides we deal with the high-spin superdeformed phenomena. By using the PSM_EO program, the Projected Shell Model is applied to the odd (even-odd) mass nuclei Tb , including 145Tb ,147Tb ,149Tb and 151Tb . The results of theoretical calculations about the transition energy E£^, kinetic moment of inertia J(1) and dynamic moment of inertia J(2) are compared with experimental data to verify the meaning in Physics.