  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. $f=1+(a/a_\star)^{-n}$, with
$a_\star$ 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.
