The potential energy curve (PEC) of the AsN(X1 +) radical is investigated by the highly accurate valence internally contracted multireference configuration interaction method in combination with the correlation-consistent basis sets, aug-cc-pV5Z for As and aug-cc-pV6Z for N atom. The PEC is fitted to the Murrell-Sorbie function, which is used to accurately derive the spectroscopic parameters. The parameters De, Re, e, exe, e and Be are obtained to be 4.97 eV, 0.16259 nm, 1061.14, 5.4715, 0.53919, 0.003409 cm-1 respectively; which accord well with the available measurements. With the obtained PEC of AsN(X1 +), a total of 67 vibrational states are predicted when J=0 for the first time by numerically solving the radical Schrdinger equation of nuclear motion. For each vibrational state, the vibrational level, the classical turning points, the inertial rotation and the centrifugal distortion constants are completely reported for the first time.