The compared kinetics of the reactions of unsaturated alcohols and alkenes with OH radicals is a topic of great interest from both the theoretical chemistry and the atmospheric chemistry points of view. The enhanced reactivity of an unsaturated alcohol, with respect to its alkene analogue, toward OH radicals has been previously demonstrated, at 298 K, by experimental and theoretical research. In this work, a new comparative investigation of such reactions is performed for 3-buten-1-ol and 1-butene. The model assumes that the overall kinetics is governed by the first OH addition steps of the mechanism. Calculations have been performed at the DFT level, employing the BHandHLYP functional and the cc-pVDZ and aug-cc-pVDZ basis sets, and the rate coefficients have been determined on the basis of the microcanonical variational transition state theory. The rate coefficients obtained for the OH reactions with 3-buten-1-ol (kOH(31BO)) and 1-butene (kOH(1B)) at 298.15 K are lower than the experimental rate coefficient available in the literature, showing deviations of 18% and 25%, respectively. Negative temperature dependence is verified for these rate coefficients. The kOH(31BO)/kOH(1B) ratios have also been investigated as a function of the temperature, suggesting that at room temperature the unsaturated alcohol reacts with the OH radicals faster than 1-butene, by a factor of 1.2, but at higher temperatures (400-500 K), the alkene should react faster, and that the stabilization of prebarrier complexes and saddle points due to hydrogen bonds is no longer an important factor to govern the reactivity of the unsaturated alcohol toward OH radicals, with respect to the alkene analogue.