We investigate the orientation of the CO (X1∑+) molecules in the combined electrostatic and laser fields. We analyze the adiabatic and nonadiabatic interactions of the molecules with the applied laser field. It shows that the pendular energy levels induced by the laser field form the tunneling doublets which can be coupled by the applied electrostatic field. The CO molecules in the X1∑+ state with small permanent dipoles can be greatly orientated due to the coupling interaction. If the laser field is added adiabatically, the excellent orientation is achieved even at a weak electrostatic field. While in a nonadiabatic case, the molecular orientation reoccurs periodically when the laser field is turned off. Additionally, we study the dependence of the degree of the molecular orientation on the applied laser and electrostatic intensities and the molecular temperature.