We developed a gas-filled capillary with a tapered density for laser wakefield acceleration, of which the tapering was realized by employing gas feed-lines with different cross-sections. Plasma diagnostics show that the capillary plasma has a significant longitudinal density tapering and a transverse parabolic profile. By using the tapered capillary plasma, high transmission (over 90%) of laser beams, meaning good optical guiding, was observed. These results demonstrate the potential of the tapered plasma source for high-energy laser wakefield acceleration, where the dephasing problem is minimized. (C) 2013 AIP Publishing LLC.