  The power spectrum of the scalar-tensor inflation with a quadratic form Ricci
scalar coupling function $\Omega(\phi)=1-
2\phi/\phi_c+(1+\delta^2)(\phi/\phi_c)^2$ can be enhanced enough to produce
primordial black holes and generate scalar-induced gravitational waves. The
masses of primordial black holes and the frequencies of scalar-induced
gravitational waves are controlled by the parameter $\phi_c$, and their
amplitudes are determined by the parameter $\delta$. Primordial black holes
with stellar masses, planetary masses, and masses around $10^{-12} M_\odot$ are
produced and their abundances are obtained from the peak theory. The
frequencies of the corresponding scalar-induced gravitational waves are around
$10^{-9}$ Hz, $10^{-6}$ Hz, and $10^{-3}$ Hz, respectively. The primordial
black holes with masses around $10^{-12} M_\odot$ can account for almost all of
the dark matter, and the scalar-induced gravitational waves with frequencies
around $10^{-9}$ Hz can explain the NANOGrav 12.5yrs signal.

General Relativity and Quantum Cosmology