  The death of the massive stars due to supernova explosion is a key ingredient
in stellar evolution, stellar population synthesis. The electron capture (EC)
plays a vital role in supernovae explosions. According to the Shell-Model Monte
Carlo (SMMC) method, basing onthe Random Phase Approximation (RPA) and Linear
Response Theory Model (LRTM), we study the strongly screening EC rates of
nuclides $^{52, 53, 59, 60}$Fe in presupernova. The results show that the
screening rates can decrease about 18.66\%. We compare our results with those
of Fuller et al. (FFN), Aufderheide et al. (AUFD), and Nabi et al. (NKK)in the
case with and without strong electron screening(SES). For the case without SES,
our calculations are in very good agreement with those of AUFD in relatively
high density surroundings and the maximum error is within 0.35\% at
$\rho_7=100$ (e. g., even-even nuclei $^{60}$Fe). However, for odd-A
nuclei$^{59}$Fe, our rates are close to one, one, two order magnitude smaller
than those of FFN, AUFD, and NKK. For the case with SES, our screening results
are about three, two orders magnitude, and 7.27\% lower than those of FFN,
AUFD, NKK for $^{60}$Fe, respectively, and it is lower about two, two orders
magnitude, and 12.42\% than those of FFN, AUFD, NKK for odd-A nuclide
$^{59}$Fe.
