We have previously reported that the hydrogen evolution reaction (HER) in acidic water electrolysis shows a potential oscillation with amplitude of about 1 V. The oscillation, named HER oscillation, is accompanied with a periodic change in the evolution rate of hydrogen bubbles, i.e., hydrogen bubbles evolve more vigorously at low potentials than at high potentials, which has led us to propose a mechanism for HER oscillation (J. Electroanal. Chem., 713, 39 (2014)). In order to obtain a deeper insight into the mechanism of HER oscillation, this present work studies the effect of high pressure (e.g. 0.7 MPa) on the oscillation and current-potential curves. It reveals that any N-shaped negative differential resistance characteristics are not involved in HER oscillation unlike the majority of electrochemical oscillations. It also shows that a solution-stirring effect due to the hydrogen bubble evolution, which causes an enhancement of convection near the electrode surface, plays an essential role in HER oscillation. We thus conclude that the appearance of HER oscillation can be explained by considering that the enhancement occurs only at low potentials at which hydrogen bubbles evolve vigorously.