The discovery of laser wakefield acceleration in gaseous plasma was a major milestone that could lead to a significant reduction of size and cost of large electron accelerators. For higher-energy laser-driven electron acceleration guiding plasma channels were proposed, which are matched to the laser pulse parameters. For guiding a Gaussian beam, a parabolic density profile is needed, which is difficult to realize experimentally. The realistic channel profiles can be described by higher order polynomial functions which are not optimal for guiding due to the development of undesired distortions in the laser intensity envelope. However, here we show that for non-parabolic plasma channels well-defined matching conditions exist, which we call mode matching. This leads to the guiding of the fundamental mode only in the acceleration regime, where the plasma electron density is modulated by the high-intensity laser pulse. In this way we eliminate two deteriorating factors of laser wakefield acceleration, namely the mode dispersion and energy leakage. We apply this new matching condition for single-mode guiding in quasi-3D simulations to show that 10 GeV energies can be reached in a distance of less than 15 cm.