We in this paper study the generation of primordial magnetic field (PMF) in the non-singular bouncing scenario, through the coupling of the electromagnetic field to gravity. We adopt an electrodynamic model with a coupling coefficient as a function of the scale factor a, i.e. f = 1 + (a/a ) −n , with a and n > 0 being constants. The result implies that in this mechanism, the power spectrum of PMF today is always blue tilted on large scales from 1 Mpc to the Hubble length, and the observational constraints favor the ekpyrotic-bounce scenario. Furthermore, the back reaction of the energy density of PMF at the bouncing point yields theoretical constraints on the bouncing model.