Recent advances in AIoT technologies have led to an increasing popularity of utilizing machine learning algorithms to detect operational failures for cyber-physical systems (CPS). In its basic form, an anomaly detection module monitors the sensor measurements and actuator states from the physical plant, and detects anomalies in these measurements to identify abnormal operation status. Nevertheless, building effective anomaly detection models for CPS is rather challenging as the model has to accurately detect anomalies in presence of highly complicated system dynamics and unknown amount of sensor noise. In this work, we propose a novel time series anomaly detection method called Neural System Identification and Bayesian Filtering (NSIBF) in which a specially crafted neural network architecture is posed for system identification, i.e., capturing the dynamics of CPS in a dynamical state-space model; then a Bayesian filtering algorithm is naturally applied on top of the "identified" state-space model for robust anomaly detection by tracking the uncertainty of the hidden state of the system recursively over time. We provide qualitative as well as quantitative experiments with the proposed method on a synthetic and three real-world CPS datasets, showing that NSIBF compares favorably to the state-of-the-art methods with considerable improvements on anomaly detection in CPS.