Unusual earthquakes series were observed one to two hours before a very long-period (VLP) seismic pulse that happened once or twice a day, during the 2000 activity of Miyakejima volcano, Japan. The series on July 11 and 12 have particularly a clear feature. The time intervals of the earthquakes in the series decrease at a constant rate in the manner of geometric progression. The maximum amplitude of each earthquake is initially almost constant, but linearly decreases with time from few minutes before the occurrence of a VLP pulse. Hypocenters of these earthquakes are below the south-western region of the crater, and near the sea level in depth. We interpret these earthquakes series as repetition of a gradual stress accumulation, and release under the variable critical stress level. The critical stress level is first constant, but linearly decreases later.