The dark matter (DM) direct detection experiments give a strong upper bound on the DM-nucleon scattering cross section (sigma_SI). Fermionic DM models with pseudoscalar mediators evade the constraint on simga_SI thanks to the momentum suppression of sigma_SI at the tree level. However, sigma_SI is not suppressed at the loop level. In this talk, I will discuss a benchmark model called "two-Higgs doublet + a” and show sigma_SI obtained by the improved analysis at the loop level. I also discuss the theoretical constraints from the stability of the electroweak vacuum and show that the maximum value of the sigma_SI is slightly above the prospect of the LZ experiment.