Conversational context information, higher-level knowledge that spans across sentences, can help to recognize a long conversation. However, existing speech recognition models are typically built at a sentence level, and thus it may not capture important conversational context information. The recent progress in end-to-end speech recognition enables integrating context with other available information (e.g., acoustic, linguistic resources) and directly recognizing words from speech. In this work, we present a direct acoustic-to-word, end-to-end speech recognition model capable of utilizing the conversational context to better process long conversations. We evaluate our proposed approach on the Switchboard conversational speech corpus and show that our system outperforms a standard end-to-end speech recognition system.