Antiferroelectric (AFE) materials exhibit great potential in the application of high-performance dielectric energy storage capacitors due to their electric field-induced AFE-ferroelectric (FE) phase transition. However, the large hysteresis of field-induced phase transition makes it difficult to simultaneously achieve high energy-storage density (W_rec) and efficiency (η) for AFEs. This work improved the energy-storage performance of NaNbO₃-based lead-free AFE ceramics by introducing the third group Bi(Mg_0.5Ti_0.5)O₃ into 0.76NaNbO₃-0.24(Bi_0.5Na_0.5) TiO₃ to regulate its relaxation characteristics. Novel lead-free AFE ceramics, (0.76-x)NaNbO₃-0.24(Bi_0.5Na_0.5)TiO₃-xBi(Mg_0.5Ti_0.5)O₃, were prepared by a traditional solid-state reaction method. Their phase structure and microstructure as well as dielectric, energy-storage, and charge-discharge characteristics were studied. The results indicated that introduction of Bi(Mg_0.5Ti_0.5)O₃ obviously enhanced the dielectric relaxor behavior of the matrix without changing its AFE R-phase structure, which led to the significantly reduced polarization hysteresis. Especially, a linear-like polarization-field hysteresis loop with extremely-low hysteresis was obtained in the composition of x=0.050. At the same time, microstructure of the ceramic was effectively optimized, its dielectric constant decreased, and its breakdown strength had significant enhanced. As a result, a high W_rec=3.5 J/cm³ and a high η=93% were simultaneously achieved under a moderate electric field of 30 kV/mm in the x=0.050 ceramic. Moreover, the x=0.050 ceramic also exhibited excellent charge-discharge characteristics with a high-power density P_D=131(1±1%) MW/cm³, a high discharge energy density W_D=1.66(1±6%) J/cm³ and a fast discharge rate t_0.9<290 ns at 20 kV/mm. The charge-discharge properties maintained good stability within a wide temperature range of 25-125 ℃. These results indicate that 0.71NaNbO₃-0.24(Bi_0.5Na_0.5)TiO₃-0.050Bi(Mg_0.5Ti_0.5)O₃ ceramics can be expected to be applied in high-power energy-storage capacitors.