Rift Valley fever virus (RVFV) is a mosquito-transmitted bunyavirus that can cause substantial morbidity and mortality in livestock and humans, for which there are no currently available licensed human therapeutics or vaccines. Therefore, the development of safe and effective antivirals is both necessary and urgent. The Gc protein is the primary target of the neutralizing antibody response related to Rift Valley fever virus. Here, we report one Gc-specific neutralizing antibody (NA137) isolated from an alpaca and one bispecific antibody (E2-NA137), the protective efficacies of which we evaluated in A129 mice. In this prophylactic study, the survival rates of the NA137 and E2-NA137 groups were both 80%, and in the treatment study, the survival rates were 20% and 60%, respectively. Altogether, our results emphasize that NA137 and E2-NA137 provide a potential approach for treating RVFV either prophylactically or therapeutically.