This paper calculates the equilibrium structure and the potential energy functions of the ground state (X2∑+) and the low lying excited electronic state (A2∏) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency (ωe) and other spectroscopic constants (ωeχe, βe and αe) are calculated by employing the Rydberg-Klein-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional Schrodinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.