Considering the different displacement boundary condition, the model of 2D-FGM plate with temperature independency of material properties was established, and the cooling transient thermal stress field distribution pictures were obtained with the finite element method. Effects on the transient thermal tress of 2D-FGM plate with temperature independency of material properties of during cooling process that the displacement boundary condition made were influential enormously. The thermal stress σx of on the free boundary of the 2D-FGM plate under simple supported and under one end clamped is zero; The thermal stresses accumulation were formed on the middle and lower of the two left and right boundaries of the 2D-FGM plate under two ends clamped, at the same time the shape and values of the thermal stress changed tremendously; To the 2D-FGM plate under clamped all around, the growth rate of the thermal stresses was more obvious than that of the 2D-FGM plate under two ends clamped. The results of this paper provide the foundations of theory calculation for the design and fabrication of the material.