Multivariate Time Series (MTS) anomaly detection focuses on pinpointing samples that diverge from standard operational patterns, which is crucial for ensuring the safety and security of industrial applications. The primary challenge in this domain is to develop representations capable of discerning anomalies effectively. The prevalent methods for anomaly detection in the literature are predominantly reconstruction-based and predictive in nature. However, they typically concentrate on a single-dimensional instance level, thereby not fully harnessing the complex associations inherent in industrial MTS. To address this issue, we propose a novel self-supervised hierarchical contrastive consistency learning method for detecting anomalies in MTS, named HCL-MTSAD. It innovatively leverages data consistency at multiple levels inherent in industrial MTS, systematically capturing consistent associations across four latent levels-measurement, sample, channel, and process. By developing a multi-layer contrastive loss, HCL-MTSAD can extensively mine data consistency and spatio-temporal association, resulting in more informative representations. Subsequently, an anomaly discrimination module, grounded in self-supervised hierarchical contrastive learning, is designed to detect timestamp-level anomalies by calculating multi-scale data consistency. Extensive experiments conducted on six diverse MTS datasets retrieved from real cyber-physical systems and server machines, in comparison with 20 baselines, indicate that HCL-MTSAD's anomaly detection capability outperforms the state-of-the-art benchmark models by an average of 1.8\% in terms of F1 score.