Binding energies of the CH3O radical on hexagonal water ice (I-h) and amorphous solid water (ASW) were calculated using the ONIOM(QM:MM) method. A range of binding energies is found (0.10-0.50 eV), and the average binding energy is 0.32 eV. The CH3O radical binding on the ASW surfaces is stronger than on the I-h surfaces. The computed binding energies from the ONIOM(wB97X-D/def2-TZVP:AMBER) and wB97X-D/def2-TZVP methods agree quite well. Therefore, the ONIOM(QM:MM) method is expected to give accurate binding energies at a low computational cost. Binding energies from the ONIOM(wB97X-D/def2-TZVP:AMBER) and ONIOM(wB97X-D/def2-TZVP:AMOE-BA09) methods differ noticeably, indicating that the choice of force field matters. According to the energy decomposition analysis, the electrostatic interactions and Pauli repulsions between the CH3O radical and ice play a crucial role in the binding energy. This study gives quantitative insights into the CH3O radical binding on interstellar ices.