Rift Valley fever virus (RVFV) is an emergent arthropod-borne zoonotic infectious viral pathogen which causes fatal diseases in the humans and ruminants. Currently, no effective and licensed vaccine is available for the prevention of RVFV infection in endemic as well as in non-endemic regions. So, an immunoinformatics-driven genome-wide screening approach was performed for the identification of overlapping CD8+ and CD4+ T-cell epitopes and also linear B-cell epitopes from the conserved sequences of the nucleocapsid (N) and glycoprotein (G) of RVFV. We identified overlapping 99.39% conserved 1 CD8+ T-cell epitope (MMHPSFAGM) from N protein and 100% conserved 7 epitopes (AVFALAPVV, LAVFALAPV, FALAPVVFA, VFALAPVVF, IAMTVLPAL, FFDWFSGLM, and FLLIYLGRT) from G protein and also identified IL-4 and IFN-γ induced (99.39% conserved) 1 N protein CD4+ T-cell epitope (HMMHPSFAGMVDPSL) and 100% conserved 5 G protein CD4+ T-cell epitopes (LPALAVFALAPVVFA, PALAVFALAPVVFAE, GIAMTVLPALAVFAL, GSWNFFDWFSGLMSW, and FFLLIYLGRTGLSKM). The overlapping CD8+ and CD4+ T-cell epitopes were bound with most conserved HLA-C*12:03 and HLA-DRB1*01:01, respectively with the high binding affinity (kcal/mol). The combined population coverage analysis revealed that the allele frequencies of these epitopes are high in endemic and non-endemic regions. Besides, we found 100% conserved and non-allergenic 2 decamer B-cell epitopes, GVCEVGVQAL and RVFNCIDWVH of G protein had the sequence similarity with the nonamer CD8+ T-cell epitopes, VCEVGVQAL and RVFNCIDWV, respectively. Consequently, these epitopes may be used for the development of epitope-based peptide vaccine against emerging RVFV. However, in vivo and in vitro experiments are required for their efficient use as a vaccine.