A new electrically driven gas booster is described as an alternative to the classical air-driven gas boosters known for their poor energetic efficiency. These boosters are used in small scale Hydrogen storage facilities and in refueling stations for Hydrogen vehicles. In such applications the overall energy count is of significance and must include the efficiency of the compression stage. The proposed system uses an electric motor instead of the pneumatic actuator and increases the total efficiency of the compression process. Two mechanical principles are studied for the transformation of the rotational motion of the motor to the linear displacement of the compressor pistons. The strongly fluctuating power of the compressor is smoothed by an active capacitive auxiliary storage device connected to the DC circuit of the power converter. The proposed system has been verified by numeric simulation, including the thermodynamic phenomena, the kinetics of the new compressor drive and the the operation of the circuits of the power smoothing system.