A silicon-based graphene modulator, holding the advantages of high modulation efficiency, high speed, and being ultra-compact, is regarded as a promising candidate for next-generation communication networks. Although the properties involved for optical communications have been widely studied, very few works evaluate the performance required for the microwave scenarios. Here, for the first time, to the best of our knowledge, the linearity of silicon-based graphene electro-absorption modulator (EAM) is analyzed and experimentally characterized through spurious free dynamic range (SFDR) with 82.5 dB·Hz1/2 and 100.3 dB·Hz2/3. Further calculations reveal that a higher SFDR value could be achieved through optimizing the bias voltage. Variations of capacitor structural parameters have little influence on the linearity. Such performance leads to the first, to the best of our knowledge, demonstration of a Gbps-level pulse-amplitude 4-level modulation scheme (PAM-4) eye diagram in a silicon-based graphene modulator.