The potential energy curves (PECs) of AsO+(X2+) and AsO+(A2) are investigated using the full valence complete active space self-consistent field (CASSCF) method through the highly accurate valence internally contracted multireference configuration interaction approach including Davidson correction (MRCI+Q). In the present calculations, the basis sets for As and O are aug-cc-pV5Z and aug-cc-pV6Z respectively. The spectroscopic parameters of the isotopes 75As16O+ and 75As18O+ are determined. The present values of Re, e, exe, e and Be for 75As16O+ (X2+) are 0.15770 nm, 1091.07 cm-1, 5.02017 cm-1, 0.514826 cm-1 and 0.003123 cm-1, respectively; the present values of Te, Re, e, exe, e and Be for 75As16O+ (A2) are 5.248 eV, 0.16982 nm, 776.848 cm-1, 6.71941 cm-1, 0.443385 cm-1 and 0.003948 cm-1, respectively, which are compared with those reported by previous investigations in the literature. And the comparison shows that excellent agreement exists between the present results and the experimentsal ones. With the PECs of AsO+ (X2+) and AsO+ (A2) determined here, the first 20 vibrational states for each electronic state are determined when the rotational quantum number J equals zero (J =0). For each vibrational state, the vibrational level G(v ), inertial rotation constant Bv and centrifugal distortion constant Dv are evaluated when J=0, which are in good accord ance with the available experimental data.