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To avoid static strength failure caused by large deflection, a design method for topology optimization of large-displacement compliant mechanisms considering global stress constraints was proposed. The Total-Lagrangian formulation and the incremental Newton-Raphson method were applied to solve the geometrically nonlinear response of the mechanisms. The element energy interpolation scheme for fictitious domain techniques was adopted to circumvent the non-convergence problem in the topology optimization of geometrical nonlinear problems. The maximum of the output displacement of the compliant mechanisms was developed as the optimization objective. The local stresses constraints for all elements were aggregated into a global stress constraint using the improved P-norm method. The optimization model for topology optimization of compliant mechanism with geometrical nonlinearities considering global stress constraints was established. The method of moving asymptotes was applied to solve the topology optimization problem for the design of large-displacement compliant mechanisms with global stress constraints. The results of numerical examples showed that large-displacement compliant mechanisms obtained by topology optimization with global stress constraint can effectively satisfy the stress constraints. As the allowable stress limit was decreased, the hinge area in the compliant mechanism configurations was gradually elongated, which can make the compliance of the mechanisms be more uniformly distributed. However, the output displacement of the mechanisms was gradually decreased.