A computational method is proposed in order to predict mechanical properties of discontinuous fiber composites (DFCs) based on computational homogenization with statistically similar representative volume elements (SSRVEs). The SSRVEs are obtained by reducing the complexity of real microstructures based on statistical measures. Specifically, they are constructed by minimizing an objective function defined in terms of differences between the power spectral density of target microstructures and that of the SSRVEs. In this paper, an extended construction method is proposed based on the reformulation of the objective function by integer design variables. The proposed method is applied to the representation of a real material, namely glass fiber reinforced nylon 6. The results show that the mechanical properties computed by numerical material tests using the SSRVEs agree with experimental results. Therefore, it is found that the nonlinear mechanical properties of the DFC can be suitably predicted by the proposed method without any special calibration to experiments performed on the composites.