Abstract: Most of the existing computational homogenization methods are based on the classical continuum theory and cannot describe the size effect. To solve this problem, a new computational homogenization method and the corresponding multi-scale analysis scheme are developed based on the consistent couple stress theory to predict the size effects of small-scale composites. Hill lemma is extended to the consistent couple stress theory, and two forms of Hill lemma are derived. According to the Hill-Mandel fine micro-macro energy equivalence condition, the average-field theory and the admissibility condition, five different sets of computational homogenization schemes are established respectively based on force-couple boundary condition, force-rotation boundary condition, displacement-couple boundary condition, displacement- rotation boundary condition and periodic boundary condition. On this basis, a finite element simulation is realized via Abaqus/UEL and Abaqus/Python, and the multi-scale analysis scheme for small-scale composites is constructed. The reliability of the scheme is verified through numerical examples. The results show that the multi-scale analysis scheme proposed in this paper has high robustness and can predict the size effect of multi-scale composites effectively.