© 2018. The American Astronomical Society. All rights reserved. We present the results of searches for gamma-ray counterparts of the LIGO/Virgo gravitational wave events using CALorimetric Electron Telescope (CALET) observations. The main instrument of CALET, CALorimeter (CAL), observes gamma-rays from ∼1 GeV up to 10 TeV with a field of view (FOV) of nearly 2 sr. In addition, the CALET gamma-ray burst monitor views ∼3 sr and ∼2π sr of the sky in the 7 keV-1 MeV and the 40 keV-20 MeV bands, respectively, by using two different crystal scintillators. The CALET observations on the International Space Station started in 2015 October, and here we report analyses of events associated with the following gravitational wave events: GW151226, GW170104, GW170608, GW170814, and GW170817. Although only upper limits on gamma-ray emission are obtained, they correspond to a luminosity of 1049 ∼ 1053 erg s-1 in the GeV energy band depending on the distance and the assumed time duration of each event, which is approximately on the order of luminosity of typical short gamma-ray bursts. This implies that there will be a favorable opportunity to detect high-energy gamma-ray emission in further observations if additional gravitational wave events with favorable geometry will occur within our FOV. We also show the sensitivity of CALET for gamma-ray transient events, which is on the order of 10-7 erg cm-2 s-1 for an observation of 100 s in duration.