Experiments for the laser guiding have been carried out with the 30-fs, 100-TW Ti:sapphier laser pulse interaction with a long slab (1.2*10 (mm)) and discharged capillary of underdense plasma. Formation of an extremely long plasma channel with its length (~10 mm) 10 times above the Rayleigh length is observed when the laser pulse power is much higher than the critical power for relativistic self-focusing. The long self-guiding channel formation is accompanied by the quasi-monoenergetic electron acceleration with a low transverse emittance (<0.8'pi' mm.mrad) and high electric current (up to ~10 nC/shot). In order to continuously elongate the plasma channel, a 4-cm-scale discharged capillary was used. We successfully demonstrated the laser-plasma acceleration of high-quality electron beams up to near GeV. Our results exactly verify the prediction of laser-wakefield acceleration through a centimeter-scale plasma channel in the "blowout bubble" regime, where a micro-scale plasma cavity produced through the ultra-relativistic laser-plasma interactions plays an essential role in the self-injection and acceleration of electrons.