The invention discloses a vacuum pressure swing adsorption system running under a stable pressure and a control process thereof. The system comprises three sets of adsorption towers, fans and vacuum pumps, each set of adsorption towers consists of two adsorption towers, and each adsorption tower circulates according to the running mode of adsorption, primary even pressure drop, secondary even pressure drop, vacuum desorption, secondary even pressure rise, primary even pressure rise and feeding. The system adopts a six-tower process, through optimal control of the process itself, two pressure equalizing is adopted in adsorption and vacuum desorption processes, and compared with the existing two-tower to five-tower process, the fluctuation range is reduced due to one more pressure equalizing, thus solving the pressure fluctuation problem of the system itself, the problems of fan outlet pressure fluctuation and vacuum pump pressure fluctuation can be solved, and the system can operate stably.