Laser-induced vibrational predesorption of molecules physisorbed on insulating substrates is theoretically investigated based on the Markoff master equation. The system vibrations, which consist of intramolecular vibrations of an admolecule and admolecule-surface vibrations, are divided by the adiabatic approximation, whereby the predesorption is represented by the nonadiabatic transitions from the bound states to the desorption continuum. By using the projection operator in the double(liouville)-space representation, the bound-continuum couplings due to the nonadiabatic and the optical interactions are explicitly included in the master equation. The adiabatic theory is applied to CO physisorbed on a NaCl(100) surface, in which CO stretching and CO-surface vibration are chosen as the system vibrations. This two-dimensional model with a shallow Morse potential for the CO-surface potential gives a desorption rate of similar to 10(-4) s(-1), which agrees with the experimentally measured rate by Chang and Ewing [Chem. Phys. 139, 55 (1989) and Phys. Rev. Lett. 65, 2125 (1990)]. The rate equations explicitly derived from the master equation are used to analyze the desorption dynamics. It is shown that predesorption is considerably enhanced by the incoherent phonon-assisted predesorption mechanism, i.e., by thermal excitation of the CO-surface stretching in the manifold of the excited CO stretching. Excitation by a single laser is extended to the two-laser excitation scheme to accelerate the predesorption.