We demonstrate on-chip octave-spanning supercontinuum (SC) generation with a Si-wire waveguide (SWG). We precisely controlled the SWG width so that the group velocity becomes flat over a wide wavelength range. By adjusting the SWG length, we could reduce the optical losses due to two-photon absorption and pulse propagation. In addition, for efficient coupling between the laser pulse and waveguide, we fabricated a two-step inverse taper at both ends of the SWG. Using a 600-nm-wide SWG, we were able to generate a broadband SC spectrum at wavelengths from 1060 to 2200 nm at a -40 dB level with only 50-pJ laser energy from an Er-doped fiber laser oscillator. We found that we can generate an on-chip broadband SC spectrum with an SWG with a length even as small as 1.7 mm.