For better utilization of the faulty operation data, supervised learning methods have recently been adopted in process monitoring and fault diangosis. However, most previously developed methods assume that all types of faults are known. Meanwhile, the data non-Gaussianity, which is often observed in multimode process measurements, cannot be handled. In this paper, a modified mixture discriminant analysis (MMDA) method is proposed to achieve better online monitoring efficiency and more accurate diagnosis. The non-Gaussian distributed process data are well modeled, while both known and unknown faults are identified. The application results on the Tennessee Eastman (TE) process verify the superiority of the proposed approach.