  According to the Shell-Model Monte Carlo method, basing on the Random Phase
Approximation and the linear response theory, we carried out an estimation on
electron capture of strongly screening nuclides $^{56}$Fe, $^{56}$Co, $^{56}$Ni
, $^{56}$Mn ,$^{56}$Cr and $^{56}$V in strong electron screening (SES)in
presupernova. The
  EC rates are decreased greatly and even exceed $21.5\%$ in SES. We also
compare our results with those of Aufderheide (AFUD), which calculated by the
method of Aufderheide in SES. Our results are agreed reasonably well with AUFD
at higher density-temperature surroundings (e.g. $\rho_7>60, T_9=15.40$) and
the maximum error is $\sim $0.5$\%$. However, the maximum error is $\sim
$13.0$\%$ at lower density surroundings (e.g. $^{56}$Cr at $\rho_7=10,
T_9=15.40, Y_e=0.41$ ). On the other hand, we also compared our results in SES
with those of FFN's and Nabi's, which is in the case without SES. The
comparisons show that our results are lower more than one order magnitude than
FFN's, but about $7.23\%$ than Nabi's.
