ASTRO-H is the next generation JAXA X-ray satellite, intended to carry instruments with broad energy coverage and exquisite energy resolution. The Soft Gamma-ray Detector (SGD) is one of ASTRO-H instruments and will feature wide energy band (40-600 keV) at a background level 10 times better than the current instruments on orbit. SGD is complimentary to ASTRO-H's Hard X-ray Imager covering the energy range of 5-80 keV. The SGD achieves low background by combining a Compton camera scheme with a narrow field-of-view active shield where Compton kinematics is utilized to reject backgrounds. The Compton camera in the SGD is realized as a hybrid semiconductor detector system which consists of silicon and CdTe (cadmium telluride) sensors. Good energy resolution is afforded by semiconductor sensors, and it results in good background rejection capability due to better constraints on Compton kinematics. Utilization of Compton kinematics also makes the SGD sensitive to the gamma-ray polarization, opening up a new window to study properties of gamma-ray emission processes. The ASTRO-H mission is approved by ISAS/JAXA to proceed to a detailed design phase with an expected launch in 2014. In this paper, we present science drivers and concept of the SGD instrument followed by detailed description of the instrument and expected performance.