We investigate the transitions between energy levels and parity symmetry in an effective two-level polar molecule system strongly coupled with a quantized harmonic oscillator. By the dressed-state perturbation theory, the transition diagrams between the dressed-state energy levels are presented clearly and show that the odd (even) parity symmetry is broken by the permanent dipole moment (PDM) of the polar molecules. By the analytical and numerical methods, we find that when the coupling strength and the PDM increase, the more frequency components are induced by the counter-rotating terms and PDM.