Proteasome is the major component of the crucial non-lysosomal protein degradation pathway in the cells, but the detailed reaction pathway is unclear. In this study, first-principles quantum mechanical/molecular mechanical free energy calculations have been performed to explore, for the first time, possible reaction pathways for proteasomal proteolysis/hydrolysis of a representative peptide, succinyl-leucyl-leucyl-valyl-tyrosyl-7-amino-4-methylcoumarin (Suc-LLVY-AMC). The computational results reveal that the most favorable reaction pathway consists of six steps. The first is a water-assisted proton transfer within proteasome, activating Thr1-O-gamma. The second is a nucleophilic attack on the carbonyl carbon of a Tyr residue of substrate by the negatively charged Thr1-O-gamma, followed by the dissociation of the amine AMC (third step). The fourth step is a nucleophilic attack on the carbonyl carbon of the Tyr residue of substrate by a water molecule, accompanied by a proton transfer from the water molecule to Thr1-N-2. Then, Suc-LLVY is dissociated (fifth step), and Thr1 is regenerated via a direct proton transfer from Thr1-N-2 to Thr1-O-gamma. According to the calculated energetic results, the overall reaction energy barrier of the proteasomal hydrolysis is associated with the transition state (TS3(b)) for the third step involving a water-assisted proton transfer. The determined most favorable reaction pathway and the rate-determining step have provided a reasonable interpretation of the reported experimental observations concerning the substituent and isotopic effects on the kinetics. The calculated overall free energy barrier of 18.2 kcal/mol is close to the experimentally derived activation free energy of similar to 18.3-19.4 kcal/mol, suggesting that the computational results are reasonable.