The potential energy curves (PECs) of 74 Omega states generated from the 21 Lambda-S states of AsN molecule are studied for the first time for internuclear separations from 0.1 to 1.0 nm. Of these 21 Lambda-S states, the X-1 Sigma+, a'(3)Sigma(+), 1(5)Sigma(+), 1(3)Delta, 1(3)Sigma(+), a(3)Pi, 1(5)Pi, 2(5)Sigma(+), 3(5)Sigma(+), 2(3)Delta, 2(3)Pi, 3(3)Pi, 3(5)Pi, and A(1)Pi states are found to be bound, and the 2(3)Sigma(+), 3(3)Sigma(+), 1(5)Sigma(-), 1(5)Delta, 2(5)Delta, 2(5)Pi, and 1(7)Sigma(+) states are found to be repulsive ones. The 3(3)Pi state possesses the double well. The 2(5)Sigma(+), 3(5)Sigma(+), 3(5)Pi, and 3(3)Pi states possess the shallow well. The a'(3)Sigma(+), 1(3)Sigma(-), 2(3)Pi, 1(3)Delta, 1(5)Pi, 2(5)Pi, 3(5)Pi, and 1(7)Sigma(+) states are found to be the inverted ones with the spin-orbit coupling effect taken into account. The PECs are calculated using the CASSCF method, which is followed by the internally contracted MRCI approach with Davidson correction. Core-valence correlation and scalar relativistic corrections are included. The vibrational properties are evaluated for the 2(5)Sigma(+), 3(5)Sigma(+), and 3(5)Pi states and the second well of the 3(3)Pi state. The spin-orbit coupling effect is accounted for by the state interaction method with the Breit-Pauli Hamiltonian. The PECs are extrapolated to the complete basis set limit. The spectroscopic parameters are evaluated, and compared with available measurements and other theoretical results. The Franck-Condon factors and radiative lifetimes of the transitions from the a'3 Sigma(+)(1), a(3)Pi(1), A(1)Pi(1), 1(3)Delta(1) and a(3)Pi(0-) states to the X-1 Sigma(+)(0+) state are calculated for several low vibrational levels, and some necessary discussion is performed. Analyses show that the spectroscopic parameters reported in this paper can be expected to be reliably predicted ones. (C) 2014 Elsevier Ltd. All rights reserved.