Dielectric capacitors with high energy storage performance have been actively studied for emerging applications. In this work, a series of environmental friendly lead-free relaxor ferroelectric ceramics, (1 - x)(Ba0.75Sr0.25)TiO3-xBi(Mg0.5Hf0.5)O3 with 0 ≤ x ≤ 0.5 [abbreviated as (1 - x)BST-xBMH], were synthesized by a high-temperature solid-state reaction method. The perovskite structure without any secondary phase can be obtained in samples with x ≤ 0.4. As the BMH content increases, the polarization-electric field (P-E) loop becomes slim and slanted. A large recoverable energy storage density of 4.3 J/cm3 and high energy efficiency of 92% were achieved simultaneously in 0.6BST-0.4BMH at 390 kV/cm. The fine grain morphology with minimal porosity and the high conductivity activation energy were responsible for the enhanced breakdown strength. Of particular importance is that the 0.6BST-0.4BMH ceramic shows excellent temperature stability and cycling reliability with energy density variations below 3 and 4%, respectively. In addition, the 0.6BST-0.4BMH ceramic possesses fast discharge time (∼0.59 μs) with a high power density of 3.5 MW/cm3. All these merits reveal that the lead-free 0.6BST-0.4BMH relaxor ceramic is a promising candidate for high-temperature and high-power energy storage capacitor applications.