The latest LIGO/Virgo/KAGRA observing run (O4) started on May 24 in 2023. Many ground and space instruments have participated in follow-up observation and search for electromagnetic counterparts of gravitational waves. Calorimetric Electron Telescope (CALET) on the Interna- tional Space Station has also searched for electromagnetic counterparts since the observation started in October 2015. Although CALET is a payload for direct measurement of high-energy cosmic rays, CALET has the capability to observe high-energy gamma-rays above 1 GeV with the Calorimeter (CAL) and X-rays / gamma rays in the energy range from 7 keV to 20 MeV with the CALET Gamma-ray Burst Monitor (CGBM). We searched for electromagnetic counterparts of gravitational wave events in the last LIGO/Virgo observing run (O3). Although no candidate was found in CALET data in O3, CAL and CGBM estimated upper limits of gamma-ray / X-ray flux for the gravitational waves in O3. We have been searching for electromagnetic counterparts of gravitational waves in O4 with improved and automated analysis pipelines to deal with many events with high event rates. As of the end of June 2023, the LIGO/Virgo/KAGRA collaboration reported 169 events via the GCN/LVC NOTICE, and 15 of 169 events were reported to GCN Circulars as significant events. Although CGBM and CAL searched for signals associated with the significant events, no candidates were found around the event time of the significant events. We obtained CAL upper limits for eight significant events of which localization high probability region overlapped with the CAL field of view.