  We study the process of the Primordial Black Holes (PBHs) production in the
novel framework, namely $\alpha$-attractor Galileon inflation (G-inflation)
model. In our framework, we take the Galileon function as
$G(\phi)=G_{I}(\phi)\left(1+G_{II}(\phi)\right)$, where the part $G_{I}(\phi)$
is motivated from the $\alpha$-attractor inflationary scenario in its original
non-canonical frame, and it ensures for the model to be consistent with the
Planck 2018 observations at the CMB scales. The part $G_{II}(\phi)$ is invoked
to enhance the curvature perturbations at some smaller scales which in turn
gives rise to PBHs formation. By fine-tuning of the model parameters, we find
three parameter sets which successfully produce a sufficiently large peak in
the curvature power spectrum. We show that these parameter sets produce PBHs
with masses ${\cal O}(10)M_\odot$, ${\cal O}(10^{-5})M_\odot$, and ${\cal
O}(10^{-13})M_\odot$ which can explain the LIGO events, the
ultrashort-timescale microlensing events in OGLE data, and around $0.98\%$ of
the current Dark Matter (DM) content of the universe, respectively.
Additionally, we study the secondary Gravitational Waves (GWs) in our setup and
show that our model anticipates the peak of their present fractional energy
density as $\Omega_{GW0} \sim 10^{-8}$ for all the three parameter sets, but at
different frequencies. These predictions can be located well inside the
sensitivity region of some GWs detectors, and therefore the compatibility of
our model can be assessed in light of the future data. We further estimate the
tilts of the included GWs spectrum in the different ranges of frequency, and
confirm that spectrum follows the power-law relation $\Omega_{GW0}\sim f^{n}$
in those frequency bands.
