Molecular orientation with combinations of near-single-cycle THz and non-resonant laser pulses is studied by means of optimal control simulation with CO molecules at 5K. We optimize non-resonant laser pulses with optimally determined final times while assuming fixed THz pulses and focusing on the carrierenvelope phase (CEP) effects. Although almost the same high degrees of orientation are achieved by the combined control independent of CEPs, the structures of the optimal non-resonant laser pulses considerably depend on CEPs and the central frequencies of the THz pulses. From a practical viewpoint, simplified treatments are also discussed. (C) 2015 Elsevier B.V. All rights reserved.