Quantum control is responsible for many key problems in quantum information processing, such as decoherence suppression, quantum state engineering and quantum gate, etc. In recent years quantum control has become a major topic in the fields of quantum optics and quantum information. Fast control of the state of quantum system is effective for both decoherence suppression caused by the environment and information processing in quantum state transfer and tracking. Comparing the standard Lyapunov control function with bang-bang Lyapunov control function, we design an optimized quantum Lyapunov control function, and analyse the influence of control laws on population transfer probability and control time contrastively. The simulation results indicate that the optimized quantum Lyapunov control strategy effectively shortens the control time and avoids high-frequency oscillation that occurs in bang-bang Lyapunov control, therefore, strengthens the robustness against external interference.