  The NANOGrav collaboration has published a suspected stochastic GW background
signal in its analysis of 12.5 years PTA data, so in this work, we investigate
the possibility to explain the signal by the inflationary models with
double-inflection-point. We calculate the energy spectrum of GWs induced by
scalar perturbations, and show that the curve lies in the $2\sigma$ region of
the NANOGrav constraints. In addition, we analyze the reheating process and
dark matter production by assuming that the inflaton is coupled with the SM
Higgs boson and singlet fermionic dark matter field. We discuss the radiative
stability of the inflationary potential under one-loop corrections, calculate
the reheating temperature, the dark matter production, and constraints the
coupling parameters using the bounds of BBN, Lyman-$\alpha$, etc.
