In this paper, we present a new identity-based encryption (IBE) system that is named Backward Compatible Identity-based Encryption (BC-IBE). Our BC-IBE is proposed to solve the problem caused by the out-of-synchronization between users’ private keys and ciphertexts. Encryption systems such as revocable IBE or revocable Attribute-based Encryption (ABE) often require updating private keys to revoke users after a certain time period. However, in those schemes, an updated key can be used to decrypt the ciphertexts created only during the current time period. Once the key is updated and the previous keys are removed, the user, the owner of the updated key, will lose access to the past ciphertexts. In our paper, we propose BC-IBE that supports backward compatibility, to solve this problem. In our proposed system, user’s private keys and ciphertexts can be updated periodically with time tags, and these processes can be used to revoke users who do not receive an updated key as the other revocable encryption does. However, in our proposed system, a private key newly issued to a user is backward compatible. This means that it decrypts not only the ciphertexts at the present time period but also all past ciphertexts. This implies that our proposed scheme guarantees the decryption of all encrypted data even if they are not synchronized. Compared to the existing revocable identity-based encryption system, our proposed BC-IBE has the advantage of simplifying key management and securely delegating ciphertext updates. Our proposed scheme only requires a single backward-compatible private key to decrypt all past ciphertexts created. Moreover, the ciphertext update process in our proposed scheme does not require any special privileges and does not require decryption. This means that this process can be securely delegated to a third-party server, such as a cloud server, and it prevents the potential leakage of secrets. For those reasons, BC-IBE is suitable for a system where users are more dynamic, such as the Internet-of-Things (IoT) network, or a system that regularly updates the data, like cloud data storage. In this paper, we provide the construction of BC-IBE and prove its formal security.