Methane/hydrogen fuels are widely applied in the internal combustion engine and gas turbine due to enhanced laminar burning velocity and extended flammability limits. In order to ensure energy utilization in safety, the flame characteristics and explosion pressure in the lean, stoichiometric and rich mixture are investigated systematically by varying hydrogen addition and initial pressure. In the lean and stoichiometric mixture, effects of the diffusional-thermal and hydrodynamic instability on flame destabilization are enhanced with hydrogen addition. As initial pressure increase, the diffusional-thermal instability has a limited effect on flame destabilization while effects of the hydrodynamic instability continue to enhance. In the rich mixture, effects of the diffusional-thermal instability on the flame stabilization and effects of the hydrodynamic instability on the flame destabilization enhance significantly with hydrogen addition. As initial pressure increase, effects of the diffusional-thermal instability on the flame stabilization are very limited and effects of the hydrodynamic instability on the flame destabilization are enhanced. The variation in maximum explosion pressure could be neglected with hydrogen addition due to decreasing heat loss, and maximum pressure rise rate increases with hydrogen addition. Besides, explosion pressure evolution could be evaluated accurately by considering the flame instabilities. And by varying equivalence ratio, hydrogen addition and initial pressure, the most enhancing and inhibiting reactions to laminar flame velocity are H + O-2 = O + OH and H + CH3(+M)=CH4(+M), respectively.