Nowadays, users/patients may gain desired medical services on-line because of the rapid development of computer network technologies. Conventional healthcare services are provided by a single server. However, care team collaboration by integrating services is the key to improve financial and clinical performance. How a user/patient accesses desired medical services provided by multiple servers becomes a challenge to realize care team collaboration. User authentication plays an important role to protect resources or services from being accessed by unauthorized users. In this paper, we first discuss the perceived security drawbacks of pervasive smart-card-based remote user authentication schemes. Then, we propose a novel dynamic-ID-based user authentication scheme based on elliptic curve cryptosystem (ECC) for multi-server environment with smart cards. The proposed scheme ensures user anonymity and computational efficiency and complies with essential requirements of a secure smart-card-based authentication scheme for multi-server environment to enable care team collaboration.