The accuracy of harmonic detection in the real power grid is not high enough at present. So a 6-term cosine window with maximum sidelobe decay which is applied into the FFT algorithm is analyzed, and an improved FFT method for harmonic detection based on 6-term cosine window and quadruple-spectrum-line interpolation is proposed. The applicable rectification formula of the quadruple-spectrum-line interpolation is obtained by using polynomial curve fit functions so that calculating burden is reduced. The simulation results show that in the algorithm the analysis precision is better than 4-term Nuttall window and 4-term Rife-Vincent window interpolated FFT in the 21 orders harmonics. Simultaneously, the precision of quadruple-spectrum-line interpolation is also better than that of triple-spectrum-line interpolation correction algorithm when the same window is used. At last the results of experiment verify that detection accuracy will be kept high when facing the noise interferences that may be encountered in real grid. This work is supported by The Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (No. KJ2015QT007).