Pulsation absorption device comprising a pressure vessel, a bladder housed in the pressure vessel, liquid incoming and outgoing paths formed by dual cylinders placed under the pressure vessel, a valve system for opening and closing said liquid incoming and outgoing paths, said valve system includes a dash pot means for slowly opening and closing a valve body whereupon the valve body is controlled from being abruptly moved with rapid streaming speed of high pressure liquid or pressure variation thereby the function of pulsation absorption is more enhanced and any trouble and damage to the pressure accumulator system is avoided.