Abstract: Using super - symmetric quantum mechanics arguments，the shape invariance of the generalized Kratzer potential is discussed，and its energy eigenvalues are calculated. Both the traditional Kratzer potential and the modified Kratzer potential are the special cases of the generalized Kratzer potential. On this basis，the exact eigenvalues of the diatomic molecules such as CO and NO for various values of radial quantum number nr and angular quantum number l are calculated numerically.

Key words: generalized Kratzer potential, diatomic molecules, super - potential, shape invariance, energy eigenvalue