This paper focuses on anomaly detection for Instrumentation and Control (I&C) systems at nuclear power plants. Cybersecurity of I&C systems is significant to Nuclear Power Plants (NPPs). When the I&C systems are under cyber-attacks, not only the I&C systems themselves are sabotaged, but also the controlled physical systems may be damaged. Traditional classification-based anomaly detection models are learned from the labeled training data, including normal data instances and abnormal ones. However, during the operation of NPPs, most of the recorded data are normal whereas little abnormal data can be recorded. Therefore, the one-class classification method which assumes all the training data instances only have one class label is suitable for training the anomaly detection model of the I&C systems. A replicator neural network (RNN), as the one-class anomaly detection model, is trained by replicating the input data with one class label to the desired outputs, i.e. the target data. After the RNN training with the recorded data of normal operations, the outputs for the normal data are almost the same as the target data replicated from the inputs. Meanwhile, the outputs for the abnormal data would deviate greatly from the inputs. Therefore, the outliers significant different from normal ones will be detected by the trained RNN. The performance of the RNN-based method are evaluated on the testing datasets consisting of normal data and generated abnormal ones.