Using JRA-25 reanalysis data form 1979～2010,integrate the expression of all kinds of energy .Taking the shape of the earth into consideration, we add the weight to the zonal integral before further study. Then, we repeat the time series of all kinds of energy form 1979 ～2010. Using observational data of solar constant from 1979 to 2010, the evolution of the energy of the total atmosphere, the energy of theStroposphere atmosphere and the energy of the stratosphere energy and the relationship between the energy and solar constant have been analyzed with the spectrumSand the wavelet technique. The results of continuous spectrum indicate that the energy of the total atmosphere has a significant period of 3.7 a , and the troposphere atmosphere also has the same oscillation in the same frequency band. However, the energy of the total atmosphere has a significant period form11 to 22 a . The results of Cross spectrum indicate that the solar constant and the energy of the total atmosphere present a significant oscillation period from 4 to 11 a, the solar constant and the energy of the troposphere atmosphere present a significant oscillation period from 5.5 to 7.3 a and the solar constant and the energy of the stratosphere energy present a significant oscillation period from 3.7 to 11 a.