The antioxidant properties of 21 non-phenolic terpenoids contained in essential oil extracted from the buds of Cleistocalyx operculatus have been investigated using density functional theory (DFT)-based computational methods. The C–H bond dissociation enthalpy (BDE), proton dissociation enthalpy (PDE), proton affinity (PA), electron transfer enthalpy (ETE) and ionization energy (IE) were calculated in the gas phase and in two different solvents (water and ethanol) at the ROB3LYP/6-311++G(2df,2p)//B3LYP/6-311G(d,p) level of theory for the former and with the PM6 method for the latter. Quantum chemical descriptors like chemical potential (μ), chemical hardness (η), and global electrophilicity (ω) were calculated in order to evaluate the reactivity and stability of all studied compounds. The interaction of the HOO˙ radical with α-terpinene, an example molecule, was also studied in detail by establishing a potential energy surface (PES). As a result, a kinetic concurrence between the H-abstraction reaction at the weakest C–H bond and addition reactions at the CC double bonds was clarified. On the basis of this mechanism, the antioxidant capacity may happen via the termination-enhancing process. Among the studied compounds, α-terpinene, γ-terpinene, cembrene and abieta-7,13-diene represent potential antioxidants.