[en] We propose a method for the measurement of the carrier-envelope phases of few-cycle laser pulses using the high-order harmonic spectrum from asymmetric molecules. Driven by few-cycle laser pulses, the multichannel high-order harmonic generation from asymmetric molecules is dramatically affected by the carrier-envelope phase. Usually, there are two plateaus in the high-order harmonic spectrum and the first cutoff extends almost linearly with the increase of the carrier-envelope phase in the period of $-<!--\; ???\; -->0.2\mathrm{\pi <!--\; ??\; -->}⩽<!--\; ???\; -->\mathrm{\varphi <!--\; ??\; -->}<<!--\; <\; -->1.8\mathrm{\pi <!--\; ??\; -->}$. These features are not very sensitive to the internuclear distance and can be used as a tool for the measurement of the carrier-envelope phase. Both the classical and quantum-mechanical analysis are performed and the results agree well. (paper)