The Calorimetric Electron Telescope (CALET) was installed onboard the International Space Station in August 2015 and since October 2015 it is collecting data with smooth and continuous operations. The instrument consists of two layers of segmented plastic scintillators to identify the charge of individual elements from proton to iron, a thin imaging tungsten scintillating fiber calorimeter providing accurate particle tracking and complementary charge measurement, and a thick total absorption calorimeter made of lead-tungstate crystal logs. In addition to high preci- sion measurements of the electron spectrum up to several TeV, CALET can measure the individual spectra and elemental composition of cosmic-ray nuclei from few tens of GeV to the PeV scale, which is of fundamental importance to shed light on the mechanism of acceleration and propaga- tion of cosmic rays in the Galaxy. In this paper, preliminary measurements of the energy spectra of carbon and oxygen, based on the first three years of collected data, will be presented.