Abstract: With the algebraic method of studying the full vibrational energy and precise vibrational spectrum constants in diatomic molecules and ions systems, a series of precise vibrational spectrum constants and full vibrational energy spectrum were generated based on a number of experimentallymeasured lower vibrational energy levels of ¹²C¹⁶O. The ground states spectrum constants of ¹²C¹⁸O and ¹³C¹⁶O and the isotope shift of them have also been obtained by combining algebraic method with the Herzberg’s isotope effect theory, which may be important and useful for the experiment measurements.