Detecting anomalies in time series has become increasingly challenging as data collection technology develops, especially in real-world communication services, which require contextual information for precise prediction. To address this challenge, researchers usually use time-series decomposition to reveal underlying patterns, e.g., trends and seasonality. However, existing decomposition-based anomaly detectors do not explicitly consider such contextual information, limiting their ability to correctly detect contextual cases. This paper proposes Time-CAD, a new context-aware deep time-series decomposition framework to detect anomalies for a more practical scenario in real-world businesses. We verify the effectiveness of the novel design for integrating contextual information into deep time-series decomposition through extensive experiments on four real-world benchmarks, demonstrating improvements of up to in time-series aware score on average.