SARS-CoV-2 (Severe acute respiratory syndrome coronavirus-2) is a newly emerged beta coronavirus and etiolating agent of COVID-19. Considering the unprecedented increasing number of COVID-19 cases, the World Health Organization declared a public health emergency internationally on 11th March 2020. However, existing drugs are insufficient in dealing with this contagious virus infection; therefore, a vaccine is exigent to curb this pandemic disease. In the present study, B- and T-cell immune epitopes were identified for RdRp (RNA-dependent RNA polymerase) protein using immunoinformatic techniques, which is proved to be a rapid and efficient method to explore the candidate peptide vaccine. Subsequently, antigenicity and interactions with HLA (human leukocyte antigen) alleles were estimated. Further, physicochemical properties, allergenicity, toxicity, and stability of RdRp protein were evaluated to demonstrate the specificity of the epitope candidates. Interestingly, we identified a total of 36 B-cell and 16 T-cell epitopes using epitopes predictive tools. Among the predicted epitopes, 26 B-cell and 9 T-cell epitopes showed non-allergenic, non-toxic, and highly antigenic properties. Altogether, our study revealed that RdRp of SARS-CoV-2 (an epitope-based peptide fragment) can be a potentially good candidate for the development of a vaccine against SARS-CoV-2.