Along with the rapid development of space exploration, communication and earth observation technology, the large space membrane structure gains its widely application. With poor stiffness and large flexibility, the surface accuracy of membrane structures can be easily interfered by the space environment variety, so precise shape control of in-orbit space membrane reflector becomes the focus in space technology area. As an object for this paper, the active control of the membrane reflector deformation under typical thermal disturbance in space is investigated. Considering of Von-Karman geometrical nonlinearity, the equilibrium equations of a circular membrane are firstly presented based on Hamilton’s Principle and Love’s thin shell theory. As a simplification for equilibrium equations, the nonlinear mathematical model for the circular membrane in a symmetrical temperature field is obtained. In the next place, an FE model for a circular membrane under thermal load is developed in Abaqus as an example. By contrasting the FEM deformation analysis with mathematical modeling solutions of circular membrane reflectors under typical thermal load, it is demonstrated that the theoretical model is capable of predicting the amplitude of membrane surface deformation. At last, a boundary actuation strategy for membrane shape control is proposed, which could effectively decrease the membrane wrinkle induced by thermal disturbance via precisely control to the tension of the SMA wire actuators. The simulation result indicates the effectiveness of boundary active control strategy on improving membrane surface accuracy with different temperature distributions. The conclusions of modeling and analysis in this paper will be an essential theoretical foundation for future research on active flatness control for in-orbit large space membrane structure.