Early-stage fault detection and diagnosis of distillation has been considered an essential technique in the chemical industry. In this paper, fault diagnosis of a distillation column is formulated as an inverse problem. The nonlinear least squares algorithm is used to evaluate fault parameters embedded in a nonlinear dynamic model of distillation once abnormal symptoms are detected. A partial least squares regression model is built based on fault parameter history to explicitly predict the development of fault parameters. With the stripper of Tennessee Eastman process as example, this novel approach is tested for step- and random-type faults and several factors affecting its efficiency are discussed. The application result shows that the hybrid inverse problem approach gives the correct change of fault parameter at a speed far faster than the base approach with only a nonlinear model.