We report results of a search for light weakly interacting massive particle (WIMP) dark matter from the CDEX-1 experiment at the China Jinping Underground Laboratory (CJPL). Constraints on WIMP-nucleon spin-independent (SI) and spin-dependent (SD) couplings are derived with a physics threshold of 160 eVee, from an exposure of 737.1 kg-days. The SI and SD limits extend the lower reach of light WIMPs to 2 GeV and improve over our earlier bounds at WIMP mass less than 6 GeV.