Nine low-lying electronic states of the AsP molecule, including \Sigma+, \Pi, and \Delta symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method. The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present. Three quintet states are reported for the first time. Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.