We have designed a high-efficiency broadband grating coupler for coupling between silicon-on-insulator (SOI) waveguides and optical fibers. The grating is only 13 microm long and 12 microm wide, and the size of the grooves is optimized numerically. For TE polarization the coupling loss to single-mode fiber is below 1 dB over a 35-nm wavelength range when using SOI with a two-pair bottom reflector. The tolerances to fabrication errors are also calculated.