TLS is the most widely deployed security protocol, however, it can only secure the applications that are based on reliable transport. Datagram TLS (DTLS) is a modified version of the TLS protocol which provides security protection in datagram environments. In DTLS, however, the communication parties need complete authentication though the certification authority when they establish connection. Consequently, the connection establishment process takes long time with a high security overhead, which cannot meet the requirement for resource-constrained network communication environment such as Internet of Things. This paper introduces identify-based cryptography to DTLS. It provides authentication while calculating the session key, and avoids the overhead associated with handling certificates in the handshake protocol. The paper designs a new DTLS handshake protocol, which reduces the number of interactions and messages, and shortens the connection establishment time. Experimental results show that the DTLS with identity-based cryptography reduces the communication setup time by nearly 50% without compromising the security.