Network or physical attacks on industrial equipment or computer systems may cause massive losses. Therefore, a quick and accurate anomaly detection (AD) based on monitoring data, especially the multivariate time-series (MTS) data, is of great significance. As the key step of anomaly detection for MTS data, learning the relations among different variables has been explored by many approaches. However, most of the existing approaches do not consider the heterogeneity between variables, that is, different types of variables (continuous numerical variables, discrete categorical variables or hybrid variables) may have different and distinctive edge distributions. In this paper, we propose a novel semi-supervised anomaly detection framework based on a heterogeneous feature network (HFN) for MTS, learning heterogeneous structure information from a mass of unlabeled time-series data to improve the accuracy of anomaly detection, and using attention coefficient to provide an explanation for the detected anomalies. Specifically, we first combine the embedding similarity subgraph generated by sensor embedding and feature value similarity subgraph generated by sensor values to construct a time-series heterogeneous graph, which fully utilizes the rich heterogeneous mutual information among variables. Then, a prediction model containing nodes and channel attentions is jointly optimized to obtain better time-series representations. This approach fuses the state-of-the-art technologies of heterogeneous graph structure learning (HGSL) and representation learning. The experiments on four sensor datasets from real-world applications demonstrate that our approach detects the anomalies more accurately than those baseline approaches, thus providing a basis for the rapid positioning of anomalies.