Fizeau demonstrated in 1850 that the speed of light can be modified when it is propagating in moving media. Can we achieve such control of the light speed efficiently with a fast-moving electron media by passing electrical current? Because the strong electromagnetic coupling between the electron and light leads to the collective excitation of plasmon polaritons, it will manifest as the plasmonic Doppler effect. Experimental observation of the plasmonic Doppler effect in electronic system has been challenge because the plasmon propagation speed is much faster than the electron drift velocity in conventional noble metals. Here, we report direct observation of Fizeau drag of plasmon polaritons in strongly biased graphene by exploiting the high electron mobility and the slow plasmon propagation of massless Dirac electrons. The large bias current in graphene creates a fast drifting Dirac electron medium hosting the plasmon polariton. It results in nonreciprocal plasmon propagation, where plasmons moving with the drifting electron media propagate at an enhanced speed. We measure the Doppler-shifted plasmon wavelength using a cryogenic near-field infrared nanoscopy, which directly images the plasmon polariton mode in the biased graphene at low temperature. We observe a plasmon wavelength difference up to 3.6% between plasmon moving along and against the drifting electron media. Our findings on the plasmonic Doppler effect open new opportunities for electrical control of non-reciprocal surface plasmon polaritons in nonequilibrium systems.