An ab initio chemical kinetics study of the reactions of methyl butanoate (MB) with hydroperoxyl radical (HO2) is presented in this paper. Particular interest is placed on determining the influences of torsional anharmonicity and addition reaction on the rate constants of hydrogen abstraction reactions. Stationary points on the potential energy surface of MB + HO2 are calculated at the level of QCISD(T)/CBS//B3LYP/6-311++G(d,p). The transition state theory (TST) is used to calculate the high-pressure limit rate constants of the hydrogen abstraction reactions over a board range of temperature (500-2000 K). Anharmonicity of low-frequency torsional modes is considered in the rate calculations by using the one-dimensional hindered rotor approximation and the internal-coordinate multistructural approximation; the latter is used as a higher-level theoretical method to examine the applicability of the former in dealing with strongly coupled torsional modes. The calculated rate constants are compared with the available data from the literature and observed discrepancies are analyzed in detail. An energetically lowest-lying addition reaction with subsequent isomerization and decomposition reactions are identified on the potential energy surface. The multiple-well Master equation analysis shows that these reactions have a secondary influence on the rate constants in the temperature range of interest.