Canonical variate analysis (CVA) has been extensively applied in monitoring of different industrial processes. However, conventional CVA is unable to handle the characteristics of time-varying processes. It tends to interpret the natural changes of the process as faults, which would cause high false alarm rates. To solve this problem, a recursive canonical variate analysis based on the first order perturbation theory (RCVA-FOP) is proposed to detect faults in time-varying processes. Without recalling past training data, the covariance of past observation vectors is updated by the exponential weighted moving average (EWMA) method. Moreover, the first order perturbation theory is introduced to realize the recursive singular value decomposition (SVD) of the Hankel matrix, which can reduce computational time significantly compared with the conventional SVD. To identify the real reason for a fault, an EWMA contribution plot based on CVA is also proposed to enhance the fault identification rate. The proposed method is verified with simulations of the continuous stirred tank reactor. Simulation results indicate that the RCVA-FOP method not only can effectively adapt to the natural changes of time-varying processes but also can detect and identify three types of faults, which include sensor precision degradation, heat exchanger fouling fault, and sensor bias.