Abstract: A calculation model for thermal deformation and thermal stress of orthotropic material was established using Element-free Galerkin method (EFG) and the discreted governing equation for thermoelastic problem of orthotropic material based on EFG method was deduced. The reliability of present model and programs have been verified through a numerical example of composite cooling grid. The total thermal deformation displacement and Mises stress of orthotropic materials turbine impeller with different off-angles, thermal conductivity factors, thermal expansion coefficient factors and primary and secondary Poisson's ratio factors were analyzed using the calculation model. The effects of off-angle and the above orthotropic material factors on total thermal deformation displacement and Mises stress were discussed, and the reasonable ranges of these parameters were provided. A group of parameters were selected to analyze the thermal deformation and thermal stress of orthotropic material by using the proposed calculation model and compared with isotropic materials. The results show that the calculation accuracy of total thermal deformation displacement and Mises stress based on EFG method is higher than the finite element method. The off-angle affects both magnitude and direction of total thermal deformation displacement and Mises stress, while orthotropic factors only affect the magnitude of total thermal deformation displacement and the Mises stress without affecting direction. Reasonable selection of off-angle and orthotropic material factors can effectively reduce the thermal deformation and thermal stress during the design of composite materials.