Thermal deformations and stresses due to temperature changes are the serious problems in cryogenic structures such as the torque tube in a superconducting generator, In this paper, the equations of thermal expansion coefficients expressed only by material properties and winding angles are derived for the filament wound composite tubes. The experimental results of thermal contraction of CFRP tubes are compared with those from theoretical approach. Composite tubes with optimally regulated thermal expansion coefficient are designed on the basis of the study for the torque tube in the superconducting generator with temperature distributions varying from 300K to 4.2 K. The filament winding angle of composites resisting thermal stresses properly is sought by the finite element method using layered shell elements. The results show that the composite tubes designed for the requirements in cryogenic environments can effectively cope with the thermal stress problem.