Recently interest in Internet of Things(IoT) is increasing, and a variety of the security technologies that are suitable for Internet of Things has being studied. Especially sensor network area of the device is an increased using and diversified for a low specification devices because of characteristic of the Internet of Things. However, there is difficulty in directly applying the security technologies such as the current authentication technologies to a low specification device, so also increased security threats. Therefore, authentication protocol between entities on the sensor network communication in Internet of Things has being studied. In 2014, Porambage et al. suggested elliptic curve cryptography algorithm based on a sensor network authentication protocol for advance security of Internet of Things environment, but it is vulnerability exists. Accordingly, in this paper, we analyze the vulnerability in elliptic curve cryptography algorithm based on authentication protocol proposed by Porambage et al. and propose an improved authentication protocol for sensor networks in Internet of Things environment.