We report efficient amplification of chirped supercontinuum pulses in a two-stage stimulated Raman amplifier based on double tungstate [KGd(WO4)2] crystals, pumped with 1.2 ps transform-limited pulses at a 1030 nm wavelength. The second stage demonstrates a conversion efficiency of 55% with an output pulse energy of 0.6 mJ at a 1135 nm wavelength. The amplified Stokes bandwidth is 10 times the pump bandwidth, providing 145 fs pulses after compression.