Potential energy curves (PECs) for the low-lying states of the diatomic cesium iodide cation (CsI+) have been calculated using the internally-contracted MRSDCI method with relativistic pseudopotentials. First, we calculate PECs for spin-orbit (SO)-free Lambda-S states, (2)Sigma(+) and (2)Pi, stemming from the triply degenerate P-2 state of I. Then we obtain PECs for SO-included Omega states, X3/2, 1/2(I), and 1/2(II), by diagonalizing the matrix of the electronic Hamiltonian plus SO coupling. It is found that all of the three Omega state PECs, X3/2, 1/2(I), and 1/2(II), have shallow wells with the depths of 1.4-4.6 kcal mol(-1). It is also predicted that transition dipole moments (TDMs) among these Omega states have values of non-negligible amounts around equilibrium internuclear distances and the TDMs can contribute to the optical transition between the states. In addition, ionization energies from the neutral CsI molecule to the CsI+ cation are estimated by comparing the present PECs with those for CsI obtained in our previous work [J. Chem. Phys. 128 (2008) 024301]. Agreement between theory and experiment at the equilibrium internuclear distance and at the dissociation asymptote is found to be good, suggesting the high reliability of the present calculations. (C) 2012 Elsevier B.V. All rights reserved.