Electron-capture rates in nuclei at stellar environments are evaluated by using new shell-model Hamiltonians.　A new Hamiltonian for pf-shell, GXPF1J, can describe Gamow-Teller (GT)　strengths in Ni isotopes very accurately. In particular, large spreading in the GT strength in 56Ni and 55Co obtained for GXPF1J has been confirmed by a recent experiment .The updated e-capture rates as well as beta-decay rates obtained in a large region of pf-shell nuclei are applied to study nucleosynthesis in Type-Ia supernova explosions and core-collapse supernova explosions. The e-capture rates with GXPF1J, which are generally smaller than those with conventional shell-model Hamiltonians such as KB3G and lead to less production of neutron-rich nuclei such as 58Ni and 54Cr, can thus solve the problem of over-production of neutron-rich isotopes in the Fe region compared to the solar abundance. For more neutron-rich isotopes such as 78Ni, extension of the configuration space outside the pf-shell is essential. Here, GT strength and spin-dipole strengths in 78Ni are evaluated within pf+g9/2+d5/2 shells. Core-collapse supernova explosions are sensitive to the e-capture rates for nuclei around this region . Electron-capture rates in 78Ni are discussed with shell-model as well as with RPA calculations.