This paper studies a dynamic model and active vibration control of a membrane antenna structure. Based on the finite element method (FEM), the dynamic model of the membrane antenna structure is established. Piezoelectric actuators are used to suppress the vibration of the structure and their optimal locations on the membrane are determined using the optimization method, where an efficient numerical criterion depended on controllability Grammian is used as optimization criterion and the particle swarm optimizer (PSO) is used as optimization algorithm. Active controllers are designed by the classical linear quadratic regulator (LQR) method. Simulation results indicate that the vibration modes and dynamic responses obtained by the dynamic model established in this paper coincide well with the results of the software ABAQUS; vibration of the structure can be suppressed effectively by the piezoelectric actuators, and optimal placed actuators not only can produce better control effectiveness but also need smaller control cost.