Bispectrum is a powerful tool for non-Gaussian signal processing and nonlinearity detection. However, it is difficult to use in practical applications due to that it is a 2-dimensional function. Bispectral slices are widely used reduction methods, and they can only represent a small part of the whole bispectral information. Integrated bispectrum contains more signal features than that of the bispectral slices, whereas the integration will lose the focus of some signal features. To overcome these problems, a new approach called maximal bispectrum is proposed to extract signal features. Maximal bispectrum is obtained by selecting the maximal values of every row of the magnitude bispectrum in the whole bispectral plane and it is a 1-dimensional function. Feature extraction based on maximal bispectrum is investigated and the maximal bispectrum is used to extract features of gear fault. Experimental results indicate that the maximal bispectrum is effective for diagnosing gear crack fault.