Composite materials such as particulate filler composite plastics (PFCP) are characterized by the random distribution of stiff inclusions embedded in the matrix, which has been found to have some uncertainties in their macroscopic mechanical behavior. To realize multi-scale analysis for such composite materials with nonperiodic microstructures, we explore the computational homogenization with improved minimal kinematic condition. Although the previous method enables us to deal with an arbitrary random geometry at the microscale and therefore allows for flexibility with respect to geometry modeling of the representative volume elements (RVE), it has been pointed out that there are accuracy problems in applying it to actual materials. Specifically, the method produces extremely small macroscopic stiffness compared to the conventional method and cannot reproduce the well-known analysis results for RVEs with simple geometries. This defect is particularly influential on problems involving material nonlinearities, such as elasticplastic behavior. Against this problem, we try to improve the minimal kinematic condition by providing additional constraints and incorporate it into the framework of decoupled two-scale analysis. To be more specific, after the results of numerical material testing are reflected in an assumed macroscopic constitutive equation, a macroscopic analysis is carried out and followed by localization analysis. Representative numerical examples are presented to demonstrate the appropriateness of the proposed scheme.