On the basis of considering the thermo-viscoelasticity of the epoxy matrix, the geometrically nonlinear finite element formulation is developed to simulate the moderate deflection bending of the shape memory alloy (SMA) hybrid beam upon actuation of SMA. It is found that the midpoint deflection of the epoxy beam increases with increasing temperature when temperature is lower than the austenite start temperature of SMA. Once the austenite start temperature of SMA is reached, the midpoint deflection of the epoxy beam is rapidly decreased to the initial state with the increasing of temperature. And then it increases slowly with increasing temperature after the austenite phase transformation of SMA is finished. The results based on the geometrically nonlinear finite element analysis are also compared with those from the geometrically linear finite element analysis, which shows that they agree well with each other when the bending deflection of the epoxy beam is small, while significant discrepancies occur between them when the deflection is considerably large.