The current design codes for evaluating the shear strength of concrete beams reinforced with fiber-reinforced polymer (FRP) bars predominantly rely on a semi-empirical approach through test data calibration without a robust theoretical background. This approach may lead to either overestimation or underestimation, resulting in significant scattering in strength predictions. This study proposed a modified approach to enhance the existing unified shear-strength model developed for steel-reinforced concrete (RC) beams based on the compression zone failure mechanism, for predicting the shear strength of FRP-RC beams without shear reinforcement. The proposed model integrates strain and stress approaches, accounting for the distinctive characteristics associated with FRP reinforcement. Additionally, the overall shear resistance capacity of the FRP-RC beam is considered as the sum of contributions from the intact concrete of the compression zone and the aggregate interlock mechanism. The reliability of the proposed model is verified by comparing its predictions with a comprehensive database comprising 264 FRP-RC beam specimens without shear reinforcement reported by 41 research groups. Furthermore, the accuracy of the proposed model was assessed through a comparative analysis with existing evaluation methods, encompassing machine learning-based models, empirical models, theoretical models, and design codes. The results indicate that the proposed model satisfactorily predicts the shear strength of FRP-RC beams within a wide range of design parameters. In comparison with machine learning-based models, the proposed theoretical model exhibits a similar level of accuracy in terms of the mean shear strength ratio and coefficient of determination (R2) values but with less scattering, indicated by lower coefficient of variation (COV) and root mean square error (RMSE) values. In addition, the proposed model outperforms existing empirical and theoretical models, as well as current design codes, by significantly enhancing prediction accuracy, demonstrated by lower COV, RMSE, and higher R2 values. Finally, a parametric study was conducted to investigate the effects of the key parameters on the shear strength of FRP-RC beams using both the proposed model and representative existing evaluation methods.