At J-PARC, 3 GeV protons with a power of 1 MW are injected onto a mercury target at a repetition rate of 25 Hz, producing fast neutrons via a spallation reaction. The high-energy neutrons are slowed down to thermal and/or cold neutrons in hydrogen moderators, to which supercritical hydrogen is supplied at 1.5 MPa and below 20 K. The nuclear heating is estimated to be 3.75 kW for a proton beam power of 1 MW. The pulsed cold neutron is suitable for crystal and magnetic structural analyses because it has a narrow full-width-half-maximum of approximately 100 μs and a short tail. We developed a cryogenic hydrogen system in which supercritical para-hydrogen circulates at 190 g/s and have operated it since 2008. It has the largest flow rate in the world and can reduce the moderator temperature fluctuation below 3 K. So far, we encountered several problems, although long-lasting operation for more than three months has been carried out. For example, the Great East Japan Earthquake was experienced in March 2011. The interlocking system was able to shutdown the cryogenic hydrogen system automatically as expected. In this study, we describe the operation characteristics and our experiences with the J-PARC cryogenic hydrogen system. The proton beam power was gradually increased to 500 kW in 2015. The trial of 600-kW proton beam operation was successfully achieved in April 2015. It was confirmed that the heater and accumulator developed can mitigate the pressure rise caused by the sudden heat load at the moderators when the proton beams are turned on and off. The dynamic behavior in the hydrogen loop can be also simulated using our simulation code. The pressure rise for a 1-MW proton beam is predicted to be below the allowable pressure rise of 0.1 MPa. We believe that the pressure control system is effective for use with 1-MW proton beam operation.