In this paper, a novel approach is proposed to extract features from the bispectra of mechanical fault signals using non-negative tensor factorization (NTF) for the purpose of establishing an intrinsic relationship between mechanical faults and extracted characteristics. First, the bispectra of mechanical signals are obtained and stacked to form a three-dimensional (3D) tensor. Then, an NTF method is applied to extract features, which are represented by a series of “basis images,” from this tensor. Finally, coefficients indicating these basis images’ weights in constituting original bispectral images are calculated for fault classification. Experiments on fault datasets of gearboxes showed that the results of the proposed method not only reveal some nonlinear features of the system, but also have low data dimensions and intuitive meanings with regard to fault characteristic frequencies, which bring great convenience to an explanation of the relationship between mechanical faults and the corresponding bispectra.