Recognizing isolated digits of the flight callsign is an important and challenging task for automatic speech recognition (ASR) in air traffic control (ATC). Fortunately, the flight callsign is a kind of prior ATC knowledge and is available from dynamic contextual information. In this work, we attempt to utilize this prior knowledge to improve the performance of the callsign identification by integrating it into the language model (LM). The proposed approach is named context-aware language model (CALM), which can be applied for both the ASR decoding and rescoring phase. The proposed model is implemented with an encoder–decoder architecture, in which an extra context encoder is proposed to consider the contextual information. A shared embedding layer is designed to capture the correlations between the ASR text and contextual information. The context attention is introduced to learn discriminative representations to support the decoder module. Finally, the proposed approach is validated with an end-to-end ASR model on a multilingual real-world corpus (ATCSpeech). Experimental results demonstrate that the proposed CALM outperforms other baselines for both the ASR and callsign identification task, and can be practically migrated to a real-time environment.