This paper focuses on the control design and stability analysis of a Susceptible-Exposed-Infected-Vigilant (SEIV) epidemic model via adaptive complex networks. The network is designed empirically as a state-dependent network, where the network structure keeps changing to inhibit the epidemic propagation. The recovery rate and the disease prevention rate are chosen as the control scheme in the epidemic system, both of which are closely associated with medical resources allocation. People may cut the connection with an infected neighbor and reduce the frequency to go out when an epidemic occurs. In order to formulate this behavior, an adaptive network structure is presented which is designed to be consistent with real human contact behaviors under epidemic prevalence. A candidate Lyapunov function is employed to analyze the system stability and guarantee the extinction of the epidemic. Simulation results are shown to illustrate the high efficiency and validity of the parameter control and the adaptive network design.