The CALorimetric Electron Telescope, CALET, has been measuring high-energy cosmic rays on the International Space Station since October 13, 2015. The scientific objectives addressed by the mission are to search for possible nearby sources of high-energy electrons and potential signatures of dark matter, and to investigate the details of galactic cosmic-ray acceleration and propagation. The calorimetric instrument, which is 30 radiation lengths or 1.3 proton interaction lengths thick with fine imaging capability, is optimized to measure cosmic-ray electrons by achieving large proton rejection and excellent energy resolution well into the TeV region. In addition, very wide dynamic range of energy measurement and individual charge identification capability enable us to measure proton and nuclei spectra from a few tens GeV to a PeV scale. Nearly 20 million cosmic-ray shower events over 10 GeV per month are triggered and the continuous observation has been kept without any major interruption since the start of operation. Using the data obtained over 6.5 years of operation, we will present a brief summary of the CALET observation including electron spectrum, and proton and nuclei spectra as well as the performance study on orbit with MC simulations.