Fast radio bursts (FRBs) are short duration (∼millisecond) radio transients with cosmological origin. The simple sharp features of the FRB signal have been utilized to probe two fundamental laws of physics, namey, testing Einstein's weak equivalence principle and constraining the rest mass of the photon. Recently, Hessels et al. (2018) found that after correcting for dispersive delay, some of the bursts in FRB 121102 have complex time-frequency structures that include sub-pulses with a time-frequency downward drifting property. Using the delay time between sub-pulses in FRB 121102, here we show that the parameterized post-Newtonian parameter γ is the same for photons with different energies to the level of |γ 1 − γ 2 | < 2.5 × 10 −16 , which is 1000 times better than previous constraints from FRBs using similar methods. We also obtain a stringent constraint on the photon mass, m γ < 5.1 × 10 −48 g, which is 10 times smaller than previous best limits on the photon mass derived through the velocity dispersion method.