In this study, preliminary simulations were performed to manufacture thermoplastic composites that can be processed by injection. For analysis, a basalt particulate–polymer composite model was manufactured and its elastic modulus, shear modulus, thermal expansion coefficient, and thermal conductivity were predicted using finite-element analysis (FEA) and micromechanics. Polypropylene (PP), polyamide 6, polyamide 66, and polyamide (PA) were employed as the polymer matrix, with the variations in their properties investigated based on the volume fraction of basalt. The polymer–basalt composite’s properties were analyzed effectively using FEA and the micromechanics model. FEA was performed by constructing a 3D model based on the homogenization technique to analyze the effective properties. The micromechanics model was analyzed numerically using the mixture rule, and the Mital, Guth, and Halpin–Tsai models. As a result, it is best to analyze the effective properties of polymer–basalt composites using the Halpin–Tsai model, and it is necessary to conduct a comparative analysis through actual experiments. In the future, actual composite materials need to be developed and evaluated based on the findings of this study.