A fault monitoring and diagnosis method for industrial processes based on recursive sparse principal component analysis (RSPCA) is proposed, which can be used for adaptive fault monitoring and diagnosis of time-varying industrial processes. By introducing the elastic regression net, the principal component analysis problem is changed to a convex optimization problem combining Lasso and Ridge regression. Successively, the covariance matrix is decomposed recursively by rank -1 matrix correction, which leads to the recursive updating of the sparse load matrix and the process control limit of monitoring statistics to realize the long-time adaptive fault monitoring of continuous industrial processes. With regard to the detected faults, the fault diagnosis is realized by using the contribution graph method. Experiments in Tennessee-Eastman (TE) process show that the proposed method effectively reduces the rate of failure miss detection and false alarm with low time complexity compared with traditional fault monitoring methods, which can ensures the sensitivity and real-time performance of the fault monitoring.