We calculated the rate constants for an alkoxy radical (CH3O, C2H5O and i-C3H7O) reaction with an oxygen molecule over a temperature range of 200-1000 K by means of dual-level direct dynamics, based on both the high-level ab initio theory and the variational transition state theory (VTST). We determined the potential energy surfaces at the B3LYP/6-311G(d,p) level and performed single-point calculations at the G2M(RCC1) level to obtain more accurate energies. The calculated rate constants and the temperature dependence are compared with those in the experiment. The improved canonical variational TST rate constants with small curvature tunneling correction agree reasonably well with the experimental rate constants of the CH3O + O-2 and i-C3H7O + O-2 reactions, in which only the ground-state A' alkoxy radicals react with O-2. In contrast, we suggest that both the ground electronic state A" and the low-lying excited electronic state A' ethoxy radicals participate in the reaction of C2H5O + O-2. The C2H5O + O-2 reaction rate constant calculated under this assumption is in good agreement with the experimental data. The temperature dependence of the rate constants for these reactions exhibited a non-Arrhenius behavior. It is important to note that the bottleneck of the i-C3H7O + O-2 reaction has a large variational effect and thus can be explained only by employing a theory based on the variational principle.