The Se77(n,γ) reaction is of importance for Se77 abundance during the slow neutron capture process in massive stars. We have performed a new measurement of the Se77 radiative neutron capture cross section at the Neutron Time-of-Flight facility at CERN. Resonance capture kernels were derived up to 51 keV and cross sections up to 200 keV. Maxwellian-averaged cross sections were calculated for stellar temperatures between kT=5keV and kT=100keV, with uncertainties between 4.2% and 5.7%. Our results lead to substantial decreases of 14% and 19% in Se77 abundances produced through the slow neutron capture process in selected stellar models of 15M⊙ and 2M⊙, respectively, compared to using previous recommendation of the cross section.