A classic mechanics model is presented to account for the vibration of a linear triatomic molecule. In this model，a coil spring loops two chemical bonds. The coil spring possesses the potential energy in the bending mode，rather than the longitudinal spring along the bonds. The ordinary differential equation system of this model is formulated. By solving equation system，three eigenvibration frequencies and the corresponding modes are obtained.This model is validated by the literature data of three molecules，carbon dioxide，carbonyl sulfide and hydrogen cyanide. The results indicate that three eigenfrequencies of the presented model fit the literature data well.