Anomaly detection based on system logs plays an important role in intelligent operations, which is a challenging task due to the extremely complex log patterns. Existing methods detect anomalies by capturing the sequential dependencies in log sequences, which ignore the interactions of subsequences. To this end, we propose CSCLog, a Component Subsequence Correlation-Aware Log anomaly detection method, which not only captures the sequential dependencies in subsequences but also models the implicit correlations of subsequences. Specifically, subsequences are extracted from log sequences based on components, and the sequential dependencies in subsequences are captured by Long Short-Term Memory Networks (LSTMs). An implicit correlation encoder is introduced to model the implicit correlations of subsequences adaptively. In addition, Graph Convolution Networks (GCNs) are employed to accomplish the information interactions of subsequences. Finally, attention mechanisms are exploited to fuse the embeddings of all subsequences. Extensive experiments on four publicly available log anomaly detection datasets demonstrate the effectiveness of CSCLog, outperforming the best baseline by an average of 3.97% in Macro F1-Measure