Through using potential function of diatomic molecules put forward by P.M.Morse and solving Shrdinger vibrating equation of diatomic molecules,discuss vibrating spectrum of diatomic molecules.The result shows that P.M.Morse's potential function includes the first non-harmonic term of vibration of diatomic molecule and well reflects the situation of vibration of diatomic molecules.It concludes the relationship of energy of dissociation and vibrating spectral constant.