We developed a highly accurate differential-type automatic radiation dosimeter to measure very low radiation doses. The dosimeter had two ionization chambers, each of which had a magnetically levitated electrode and it was operated in a repetitive-time integration mode. We first installed the differential-type automatic radiation dosimeter with MALICs at a high-energy electron accelerator facility (Kyushu Synchrotron Light Research Center Facility) and measured the background and ionizing radiations in the facility as well as the gaseous radiation in air. In the background dose measurements, the accuracy of the repetitive-time integration-type dosimeter was three times better than that of a commercial ionization chamber. When the radiation dose increased momentarily at the electron injection from the linac to the operating storage ring, the dosimeter with repetitive-time integral mode gave a successful response to the actual dose variation. The gaseous radiation dose in the facility was at the same level as that in Fukuoka City. We confirmed that the dosimeter with magnetically levitated electrode ionization chambers was usable in the accelerator facility, in spite of its limited response when operated in the repetitive-time integration mode.