We investigated the effects of first-forbidden transitions in ß decays on the production of the r-process peak. The theoretical calculated ß-decay rates with ß-delayed neutron emission were examined using several astrophysical conditions. As the FF decay is dominant in neutron-rich nuclei, their inclusion shortens ß-decay lifetimes and shifts the abundance peak towards higher masses. Additionally, the inclusion of the ß-delayed neutron emission results in a wider abundance peak, and smoothens the mass distribution by removing the odd–even mass staggering. The effects are commonly seen in the results of all adopted astrophysical models. Nevertheless there are quantitative differences, indicating that remaining uncertainty in the determination of half-lives for nuclei is still significant in order to determine the production of the r-process peak.