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Within the framework of inflationary model with field-dependent kinetic termfor quartic and natural potentials, we investigate generation of the primordialblack holes (PBHs) and induced gravitational waves (GWs). In this setup, weconsider a kinetic function as $G(\phi)=g_I(\phi)\big(1+g_{II}(\phi)\big)$ andshow that in the presence of first term $g_I(\phi)$ both quartic and naturalpotentials, in contrast to the standard model of inflation, can be consistent,with the 68\% CL of Planck observations. Besides, the second term$g_{II}(\phi)$ can cause a significant enhancement in the primordial curvatureperturbations at the small scales which results the PBHs formation. For theboth potentials, we obtain an enhancement in the scalar power spectrum at thescales $k\sim10^{12}~\rm Mpc^{-1}$, $10^{8}~\rm Mpc^{-1}$, and $10^{5}~\rmMpc^{-1}$, which causes PBHs production in mass scales around$10^{-13}M_{\odot}$, $10^{-5}M_{\odot}$, and $10 M_{\odot}$, respectively.Observational constraints confirm that PBHs with a mass scale of$10^{-13}M_{\odot}$ can constitute the total of dark matter in the universe.Furthermore, we estimate the energy density parameter of induced GWs which canbe examined by the observation. Also we conclude that it can be parametrized asa power-law function $\Omega_{\rm GW}\sim (f/f_c)^n$, where the power indexequals $n=3-2/\ln(f_c/f)$ in the infrared limit $f\ll f_{c}$.

Primordial black holes formation in the inflationary model with field-dependent kinetic term for quartic and natural potentials