The electronic structure of the ICl+ molecular ion is investigated by using high-level multireference configuration interaction (MRCI) method. To improve computational accuracy, Davidson corrections, spin-orbit coupling (SOC), and core-valence electron correlations effects are incorporated into the calculations. The potential energy curves (PECs) of 21 Lambda-S states associated with the two lowest dissociation limits I+(D-1(g))+Cl(P-2(u)) and I+(P-3(g))+Cl(P-2(u)) are obtained. The dipole moments (DMs) of the 21 Lambda-S states of ICl+ are systematically studied, and the variations of DMs of the identical symmetry state (2(2)Sigma(+)/3(2)Sigma(+) and 2(2)Pi/3(2)Pi) in the avoided crossing regions are elucidated by analyzing the dominant electronic configuration. When considering the SOC effect, the Lambda-S states with the same Omega components may form new avoided crossing point, making the PECs more complex. With the help of calculated SOC matrix element, the interaction between crossing states can be elucidated. Spin-orbit coupling matrix elements involving the 2(2)Pi, 3(2)Pi, 1(2)Delta and 2(2)Delta states are calculated. By analyzing potential energy curves of these states and the nearby electronic states, the possible predissociation channels for 2(2)Pi, 3(2)Pi, 1(2)Delta and 2(2)Delta states are provided. Based on the computed PECs, the spectroscopic constants of bound Lambda-S and Omega states are determined. The comparison of the spectroscopic constants between Lambda-S and Omega states indicates that the SOC effect has an obvious correction to the spectroscopic properties of low-lying states. Finally, the transition properties between excited states and the ground state are studied. Based on the computed transition dipole moments and Franck-Condon factors, radiative lifetimes for the low-lying vibrational levels of excited states are evaluated. All the data presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j 00213.00140.