Impact of the in-medium modified nucleon weak and electromagnetic form factors on the neutrino mean free path in dense matter is studied by considering both the weak and electromagnetic interactions of neutrinos with the constituents of the matter. A relativistic mean field model and the quark-meson coupling model are respectively adopted for the in-medium effective nucleon mass and nucleon form factors... We find that the cross sections of neutrino scattering in cold nuclear medium decreases when the in-medium modification of the nucleon weak and electromagnetic form factors are taken into account. This reduction results in the enhancement of the neutrino mean free path, in particular at the baryon density of around a few times of the normal nuclear matter density. The enhancement of the neutrino mean free path is estimated to be about 10--40\% compared with the values obtained without the medium modification of the nucleon form factors, and the enhancement is expected to accelerate the cooling of neutron stars. (read more)