A new topology optimization method was proposed to maximize the output displacements of multi-input-multi-output compliant mechanisms. Firstly, aconstraint function on the small quantity change of the compliance was introduced to deal with the illconditioned loads and hinge-like problems of topological optimization of multi-input-multi- output compliant mechanisms. Based on the idea of the traditional bound formula method, a new bound formula model for topology optimization of multi-input-multi-output compliant mechanisms was constructed by equivalently transforming multiple output displacement maximization objectives into multiple constraints through abound variable. Secondly, combining with the varied volume constraint scheme, density filtering technology, Heaviside mapping technology, solid isotropicmaterial inter polation method and the smooth dual algorithm, a new topology optimization method for multi-input-multi-output compliant mechanisms was proposed. The calculating results of the examples show that,compared with the existing method, the final topology obtained by proposed method is not only clear,free of hinges, but also has a larger output displacement.