Material or biological structures are analyzed through cold neutron beam scattering experiments at the Materials and Life Science Experimental Facility (MLF) at J-PARC. The high-energy MeV-order neutrons, which are produced via a spallation reaction between 3-GeV protons and the mercury nucleus, are moderated to cold neutrons with MeV-order energy by passing them through a supercritical hydrogen moderator. The cryogenic hydrogen system provides the supercritical hydrogen to a pressure of 1.5 MPa and temperature of approximately 20 K and removes the energy (nuclear heating), which is estimated to be 3.75 kW for a proton beam power of 1 MW. A kW-order heat load such as this is applied to the cryogenic hydrogen system as a step load. Therefore, to mitigate pressure fluctuation caused by the load, a pressure control system is a necessary requirement. Accordingly, a control system was designed and installed, using a heater as an active controller for thermal compensation and an accumulator as a passive volume controller. During operations at J-PARC, changes in pressure caused by operation of a 120-kW and a 302-kW proton beam were studied. When the proton beam was supplied, the pressure continuously increased until the heater control started, after which the accumulator spontaneously constricted. The heater control maintained a constant temperature downstream of the heater without any thermal disturbance. It was confirmed that the pressure control system was effective in mitigating the pressure fluctuation caused by the load. A simulation code was also developed and the pressure rise behavior and the accumulator variation were studied. The simulation results indicated good agreement with the experimental data within 10%. The pressure rise behavior and the accumulator variation were proportional to the proton beam power. The pressure fluctuation for a 1-MW proton beam was predicted to be 33.9 kPa, which was lower than the allowable pressure rise of 0.1 MPa, and produced an accumulator variation of 11.35 mm. We believe that the pressure control system is effective for use with the operation of a 1-MW proton beam.