In grinding process, chatter vibrations known as self-excited vibrations, become increasingly problematic and must be avoided. Firstly, experimental measurements of chatter vibrations in a numerical control (NC) grinding machine tool are introduced for the case of a special alloy workpiece being carried on. Then, frequency spectra of chatter vibrations are analyzed. The wavelet package transform technique is used to describe original chatter signals in the term of scaled energy of frequency bands. At last, fractal dimensions of the reconstructed signals in consecutive frequency bands of chatter vibrations are calculated. These results are helpful for understanding of the nonlinearity of chatter vibrations.