Fault diagnosis is important to the industrial process. This paper proposes an orthogonal incremental extreme learning machine based on driving amount (DAOI-ELM) for recognizing the faults of the Tennessee-Eastman process (TEP). The basic idea of DAOI-ELM is to incorporate the Gram-Schmidt orthogonalization method and driving amount into an incremental extreme learning machine (I-ELM). The case study for the 2-D nonlinear function and regression problems from the UCI dataset results show that DAOI-ELM can obtain better generalization ability and a more compact structure of ELM than I-ELM, convex I-ELM (CI-ELM), orthogonal I-ELM (OI-ELM), and bidirectional ELM. The experimental training and testing data are derived from the simulations of TEP. The performance of DAOI-ELM is evaluated and compared with that of the back propagation neural network, support vector machine, I-ELM, CI-ELM, and OI-ELM. The simulation results show that DAOI-ELM diagnoses the TEP faults better than other methods.