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Bi-stable composite shells with initial curvature have obtained much attention due to their lightweight and morphing. The twisting deformation after curing is induced by thermal residual stress generated during the manufacture of the bistable composite shells, which has a significant influence on the mechanical behavior and the cured shape of bistable composite shells with initial curvature. This paper put forward a method to control the twisting by introducing an adjustive angle. An analytical model is developed to capture the suit adjustive angle, which makes the bistable composite shells without twisting. The analytical predictions are verified by results based on the experiments and finite element results. Moreover, the effect of initial radius, ply angle, thermal expansion coefficients, and elasticity modulus on an adjustive angle is considered by the analytical model, which can provide a guide for designing the bistable composite structures without twisting. The curvatures after twisting control are provided to predict the configuration of bistable composite shells with initial curvature. • A method to control the twisting is presented by introducing an adjustive angle. • The bistable composite shells with initial curvature without twisting are obtained by twisting control. • The adjustive angle is directly proportional to the initial radius and has a nonlinearity to the ply angle. • The curvature of bistable composite shells with initial curvature without twisting is investigated. [ABSTRACT FROM AUTHOR]