Deep neural network learning is a commonly used method for fault diagnosis of the control valve. However, the catastrophic forgetting problem of deep learning in multi-task affects the fault diagnosis accuracy. Moreover, the traditional training model can be improved by using parameter constraint control or adding a few parameters, but it has many limitations. Therefore, this paper proposed a fusion of elastic weight consolidation algorithm and residual shrinkage network method, sharing common feature layers. According to the weight of the same or similar parameters of the previous task, the correct solution of the current task could be obtained, and the forgetting degree of the previous task could be reduced. It improved the generalization ability of the training model. The control valve data were collected and compared with the stochastic gradient descent algorithm in different valve openings. The results indicate that this method has a high accuracy for the condition identification of the control valve. This method can effectively alleviate the problem of the catastrophic forgetting of deep learning in multi-task identification of control valve.