  Fast radio bursts (FRBs) are milliseconds radio transients with large
dispersion measures (DMs). An outstanding question is the relation between
repeating FRBs and those with a single burst. In this paper, we study the
energy distribution of the repeating FRB 121102. For a power-law distribution
of energy $dN/dE\propto E^{-\alpha_E}$, we show that the value of $\alpha_E$ is
in a narrow range $1.6-1.8$ for bursts observed by different telescopes at
different frequencies, which indicates a universal energy distribution for FRB
121102. Interestingly, similar power-law index of energy distribution for
non-repeating FRBs observed by Parkes and ASKAP is also found. However, if
low-energy bursts below completeness threshold of Arecibo are discarded for FRB
121102, the slope could be up to 2.2. Implications of such a universal energy
distribution are discussed.
