The atmospheric Kelvin wave has been widely studied due to its importance in atmospheric dynamics. Since a long-term climatological study is absent in the literature, we have employed the two-dimensional fast Fourier transform (2D-FFT) method for the 40-year long-term reanalysis of the dataset, ERA-Interim, to investigate the properties of Kelvin waves with wavenumbers 1 (E1) and 2 (E2) at 6-24 days wave periods over the equatorial region of ±10° latitude between a 15 and 45 km altitude during the period 1979-2019. The spatio-temporal variations of the E1 and E2 wave amplitudes were compared to the information of stratospheric quasi-biennial oscillation (QBO), and the wave amplitudes were found to have an inter-QBO cycle variation that was related to sea surface temperature and convections, as well as an intra-QBO cycle variation that was caused by interactions between the waves and stratospheric mean flows. Also, the E1 waves with 6-10 day periods and the E2 waves with 6 days period were observed to penetrate the westerly regime of QBO, which has a thickness less than the vertical wavelengths of those waves, and the waves could further propagate upward to higher altitudes. In a case study of the period 2006-2013, the wave amplitudes showed a good correlation with the Nino 3.4 index, outgoing longwave radiation (OLR), and precipitation during 2006-2013, though this was not the case for the full time series. The present paper is the first report on the 40-year climatology of Kelvin waves, and the morphology of Kelvin waves will help us diagnose the anomalies of wave activity and QBO in the future.