A quantum control theory of pure state in non-ideal quantum systems is proposed in this paper. A non-ideal closed quantum systems means that the controlled quantum system is in two degenerate cases: one is at least two transition frequencies between different energy levels are the same, or/and another is at least two eigenstates of the internal Hamiltonian are not directly coupled. The implicit Lyapunov control method based on the average value of an imaginary mechanical quantity is used to design the control laws. The design procedure of the imaginary mechanical quantity is derived. The relationships among the implicit Lyapunov control methods based on the state distance, the state error and the average value of an imaginary mechanical quantity are analyzed. Finally, some numerical simulation experiments are studied.