Pulse-amplitude and fluence-specified optimal control simulation with linear (dipole) and nonlinear (polarizability) interactions is applied to find the best way to orient CO molecules with a combination of THz and laser pulses. The optimal pulses are numerically designed with a specified maximum amplitude of the THz pulse and a specified fluence of the laser pulse within the ranges of E max = 50 MV/m ∼ 150 MV/m and f 0 = 2.5 J/cm 2 ∼ 4.5 J/cm 2 at temperature T = 0 K ∼ 10 K. The optimal pulse almost always consists of a near-single-cycle THz pulse of zero area and a laser pulse that is mainly composed of three subpulses. There is no temporal overlap between the THz pulse and the laser subpulses. The THz pulse, which virtually contains no dc components, induces rotational transitions in a resonant way, whereas the three laser subpulses efficiently induce multiple rotational transitions through Raman scattering. Comparing the optimal control simulations with and without laser pulses, the laser pulses effectively increase the degrees of orientation by approximately half through the polarizability interaction with inversion symmetry.