The coupled-cluster singles-doubles-approximate-triples [CCSD(T)] theory in combination with the series of the correlation-consistent basis sets in the valence range are employed to investigate the internuclear equilibrium separations, harmonic frequencies and potential energy curves (PECs) of the HF +(X 2Π) ion. The PECs are all fitted to the Murrell-Sorbie function, which is used to determine the spectroscopic parameters ( D e , D 0, ω eχ e , α e and B e ). By comparison with the available experimental data, the PEC obtained at the basis set, aug-cc-pV5Z, is selected to investigate the vibrational manifolds. The present D e , D 0, R e , ω e , ω eχ e , α e and B e values, which are attained at the aug-cc-pV5Z basis set, are of 3.6156 eV, 3.4262 eV, 0.10011 nm, 3105.202 cm −1, 92.2546 cm −1, 0.89146 cm −1 and 17.5771 cm −1, respectively, which are in excellent agreement with the available experimental results. With the potential obtained at the UCCSD(T)/aug-cc-pV5Z level of theory, a total of 20 vibrational states is predicted when the rotational quantum number J is set to equal zero ( J = 0) by numerically solving the radial Schrödinger equation of nuclear motion. The complete vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are reproduced from the HF +(X 2Π) PEC when J = 0 for the first time.