This paper develops a sensor fault diagnosis (SFD) scheme for a multi-input and multi-output linear dynamic system under feedback control to identify different types of sensor faults (bias, drift and precision degradation), particularly for the incipient sensor faults. Feedback control, leading to fault propagation and disguised fault rectification, imposes the challenge on the data-driven SFD. With only available output data in closed loop, the proposed scheme comprises two stages of residual generation and residual evaluation. In the residual generation, a data-driven identification of the residual generator for the feedback control system is proposed. One class of parameters in the residual generator are estimated using process delays while another class of parameters describing the output dynamic are derived by the Bayes' formula. The means and variances control charts of online calculated residuals are made to judge the root cause. Two case studies are performed to illustrate the effectiveness of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.