Dielectric capacitors, although presenting faster charging/discharging rates and better stability compared with supercapacitors or batteries, are limited in applications due to their low energy density. Antiferroelectric (AFE) compounds, however, show great promise due to their atypical polarization-versus-electric field curves. Here we report our first-principles-based theoretical predictions that Bi1-xRxFeO3 systems (R being a lanthanide, Nd in this work) can potentially allow high energy densities (100-150 J cm-3) and efficiencies (80-88%) for electric fields that may be within the range of feasibility upon experimental advances (2-3 MV cm-1). In addition, a simple model is derived to describe the energy density and efficiency of a general AFE material, providing a framework to assess the effect on the storage properties of variations in doping, electric field magnitude and direction, epitaxial strain, temperature and so on, which can facilitate future search of AFE materials for energy storage.