Rational designs of electromagnetic (EM) wave absorbers with stable and well-defined chemical structures are crucial for achieving robustness and customization in the EM wave absorption frequency. Herein, we propose a controlled chemical synthesis method for well-defined fluorinated polymer modified graphene nanosheets. The minimum reflection loss frequency of modified graphene can be robustly adjusted from the high-frequency band to low frequency by altering the number of fluorine atoms. Notably, this strategy achieves up to 99.9% reflection loss across S, C, X, and Ku bands, enabling broadband EM wave absorption from 3.47 to 17.51 GHz through the modified graphene compound. Experimental results and theoretical modeling further reveal that the degree of polymer fluorination exhibits a clear positive correlation with the proportion of polarization loss in the low-frequency band. This work demonstrates a powerful chemical control method, offering a promising strategy for designing frequency-customizable EM wave absorbers with wide absorption bandwidths and well-defined structures.