The definition of Chebyshev-Fourier Moments(CHFM) was given,the performances of CHFM were investigated concisely.Tranining set of the 26 capitals of the English alphabet was normalized in the unit circle and the Chebyshev-Fourier Moments(CHFM) was calculated in unit circle.Using CHFM as recognition characters,the multi-distorted invariant pattern recognition of the alphabet was finished.The experiment was given.