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Computational homogenization is commonly used to predict the responses of composite materials. However, it poses practical issues due to large computational cost especially in the material-by-design setting when various design parameters are to be examined. This paper presents the development of a parametric model order reduction strategy for the micromechanical analysis of composites when fibre distribution is the parameter of interest. The reduced order model is obtained by applying Galerkin projection in combination with proper orthogonal decomposition. The presented framework enables a significantly reduced computational load during parametric studies as the model dimension of the microscale analyses is significantly smaller. The results show that the proposed approach can reproduce the homogenized properties of material and local stress distributions in the microstructures very well. [ABSTRACT FROM AUTHOR]