The mechanical properties of unidirectional carbon fiber reinforced polymer (UD-CFRP), such as its elastic modulus and ultimate strength, are crucial and fundamental indicators. Examining these properties from a microscopic perspective through numerical simulations can provide valuable insights for material modification and the design of new materials. This study employs a micromechanics-based representative volume element (RVE) method to predict the macroscopic mechanical properties of UD-CFRP. The results demonstrate that the established RVE models accurately predict the elastic and shear modulus, as well as the ultimate tensile and compressive strength of UD-CFRP. Additionally, simulations of 300 RVE models with varying input parameter combinations were performed, generating a dataset that encompasses both microstructure parameters and macroscopic mechanical properties of UD-CFRP. Using the dataset, random forest regression models were created and SHAP analysis was performed to identify the key microstructural parameters with significant feature importance. Subsequently, we systematically investigated their effects on the macroscopic mechanical properties of UD-CFRP. In the end, simplified analytical prediction formulas were proposed to evaluate the macroscopic mechanical properties of UD-CFRP, demonstrating superior predictive performance compared to existing formulas.