Abstract: The dynamical properties of a single molecule driven by a time dependent laser radiation field are researched. Based on the su(1,1)⊕h(3) (h(3) is Heisenberg algebra) dynamical symmetry structure of the system, the exact solutions of the system is obtained by using the algebraic dynamics method. The shift between the frequency Ω of the laser radiation field and the molecule vibration frequency ω under resonance phenomenon is studied.