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A multiscale discrete-continuum mosaic (MDCM) method for nonlinear mechanical behaviors of periodic micro/nano-scale structures is presented in this paper. The representative cell including nonlinearity and chirality of a micro/nano-scale structure can be combined with the corresponding virtual continuum counterpart for establishing the multiscale “bone-flesh” model. The moving least-square (MLS) approximation is utilized for bridging the macroscale and microscale deformation fields. Furthermore, a MDCM contact model is developed with the real discrete particles as the force points of their non-bonded van der Waals (vdW) interactions. The discreteness of the non-bonded interactions can be taken into account naturally. Based on the proposed MDCM method, a variationally consistent meshless computational scheme is constructed for simulating nonlinear mechanical responses of micro/nano-scale components. Benefiting from the order-N nature, this method can deal with large scale problems with less computational efforts.