Taking the hyperbolic doublycurved shells structure composite as the research object, the thermal buckling behavior of the composite laminated hyperbolic doublycurved shells structure under the temperature field is studied by using the finite element BlockLanczos research analysis method, and the influences of the laminated thickness, boundary conditions, fiber direction of the composite laminated hyperbolic doublycurved shells on the critical buckling temperature are studied. The results show that the critical buckling temperature of the hyperbolic doublycurved shells of composite laminates is closely related to the boundary conditions, ply thickness and fiber direction and has a certain regular distribution under uniform temperature field. Through the thermal buckling analysis of composite hyperbolic doublycurved shells structure in this paper, an effective analysis and modeling method is provided for structural design and practical application of composite Materials