  We study the generation of helical magnetic fields in a model of inflationary
magnetogenesis which is free from the strong coupling and back-reaction
problems. To generate helical magnetic fields, we add an $f^2
\tilde{F}^{\mu\nu} F_{\mu\nu}$ term to the lagrangian of Ratra model. The
strong coupling and back-reaction problems are avoided if we take a particular
behaviour of coupling function $f$, in which $f$ increases during inflation and
decreases post inflation to reheating. The generated magnetic field is fully
helical and has a blue spectrum, $d\rho_B/d\ln k \propto k^4$. This spectrum is
obtained when coupling function $f\propto a^2$ during inflation. The scale of
reheating in our model has to be lower than $4000$ GeV to avoid back-reaction
post inflation. The generated magnetic field spectrum satisfies the
$\gamma$-ray bound for all the possible scales of reheating. The comoving
magnetic field strength and its correlation length are $\sim 4 \times 10^{-11}
$ G and $70$ kpc respectively, if reheating takes place at 100 GeV. For
reheating at the QCD scales of $150$ MeV, the field strength increases to
$\sim$ nano gauss, with coherence scale of $0.6$ Mpc.
