  We investigate the proton-boron nuclear fusion cross sections under the
influence of the intense linearly polarized monochromatic laser fields with
high frequency. First, we rewrite the time-dependent Schr\"{o}dinger equation
using Kramers-Henneberger (KH) transformation which allows for shifting all
time dependence of the problem into the potential function. Then, for the
intense laser fields that satisfy the high frequency limit, the time-averaged
scheme in the KH framework should be valid. We can use WKB approximation to
evaluate Coulomb barrier penetrability and then calculate proton-boron nuclear
fusion cross sections by a phenomenological Gamow form. We show that the
corresponding Coulomb barrier penetrability increases significantly due to the
depression of the time-averaged potential barrier. As a result, we find that
proton-boron nuclear fusion cross sections can be enhanced effectively
depending on a dimensionless quantity $n_{\mathrm{d}}$, which equals the ratio
of the quiver oscillation amplitude to the geometrical touching radius of the
proton and boron nucleus. For $n_{\mathrm{d}}=9$, we predict that the resonance
peak of the fusion cross-section is enhanced by about $26$ times at the
incident energy of $\varepsilon=148$ keV. And for another incident energy of
$\varepsilon=586$ keV, the resonance peak of fusion cross-section is not only
enhanced but also shifted to lower energy of $\varepsilon=392$ keV due to the
mechanism of over-barrier fusion.
