A cyber-physical system consists of sensors, micro-controller, networks, and actuators that interact with each other, generate a substantial amount of data, and form extremely complex system operational profiles. These heterogeneous components are subject to errors, e.g. spikes, off-sets, or delays, that may result in system failures. As the complexity of modern systems increases, it becomes a challenge to apply traditional fault detection and isolation methods to such complex systems. Deep learning based methods have surpassed traditional methods in terms of performance as the data size and complexity increase. The signals of cyber-physical systems are mainly time-series data. In this paper, we propose a new on-line error detection and mitigation approach for common sensor, computing hardware, and network errors of cyber-physical systems using deep learning based methods. More specifically, we train a Long Short-Term Memory (LSTM) network as a single step prediction model for the detection and mitigation of errors, like spikes, or offsets. In order to detect the long-duration errors that show no sharp change (a sudden drop or rise) between two successive data samples when errors occurred, e.g. network delays, we train an LSTM encoder-decoder as a multi-step prediction model. We also introduce the on-line error mitigation approach. Automatic recovery is achieved by replacing the detected errors with the predicted values. Finally, we demonstrate on-line error detection and mitigation capabilities of the trained single step and multi-step predictors using representative case studies.