Dielectric capacitors, as one of the important electronic devices, are widely used in various fields. However, most ferroelectric capacitors with high energy storage density require excessively high electric fields. In this work, we have prepared 0.9(Bi0.5Na0.5)0.7Sr0.3TiO3-0.1 Bi(Mg2/3Nb1/3)O3 relaxor ferroelectric ceramics with different BaZrO3 doping levels. A high energy storage (Wr) of 4.07 J/cm3 and efficiency (η) of 91% are simultaneously obtained in 0.94[0.9(Bi0.5Na0.5)0.7Sr0.3TiO3-0.1 Bi(Mg2/3Nb1/3)O3]-0.06BaZrO3 ceramic under a medium electric field of 260 kV/cm. Additionally, the ceramic also exhibits excellent temperature and frequency stability. Furthermore, the phase field simulation is used to simulate the evolution of domain structure and hysteresis loops of the ceramics with different doping levels. The results of phase field simulation explicitly explain the influence of different relaxation degrees on energy storage density and efficiency of the ceramics. We believe that the ceramic prepared in this work is one of the most promising candidate materials for some miniaturized energy storage devices operating under low or medium electric fields.