Micro combustor is the core component of combustion-based micro power generation systems. Our recent studies showed that the combustion efficiency of lean H-2/air flames in a micro-cavity combustor deceased rapidly at high inlet velocities due to the emergence of flame tip opening. To improve this undesirable phenomenon, oxygen enrichment was employed in this study. Numerical investigations of lean H-2/O-2/N-2 flames with an equivalence ratio of 0.4 were conducted under four different oxygen proportions, i.e., x(O2) = 21%, 24%, 27% and 30%. The results demonstrate that at x(O2) = 30%, the combustion efficiency can reach up to 98.2% even at an inlet velocity of 32 m/s. The analysis reveals that as the oxygen concentration is increased, the elementary reactions and heat release are intensified considerably, whereas the stretch effect is weakened essentially at the flame tip. As a result, the occurrence of flame tip opening can be eliminated and a high combustion efficiency is thus attainable at high inlet velocities for lean H-2/N-2/O-2 flames.