This paper introduces composite microfibers that can distinguish liquid, normal, aliphatic alcohols with high selectivity. The composite microfibers are composed of a hydrophilic agarose polymer and carbon nanotube (CNT) fillers. The CNTs distributed in the CNT-agarose composite microfiber (CAF) enable the material to sensitively change its electrical conductivity upon exposure to alcohols, induced by a change in the volume of the polymer matrix. When a CAF is highly hydrated, its resistance distinctly changes depending on the molecular weight of the alcohol via competitive mass transfer of alcohol and water. As a result, highly hydrated CAFs can selectively distinguish normal, aliphatic alcohols ranging from methanol to 1-pentanol. A provisional mechanism for the alcohol-dependent change in resistance of hydrated CAFs is suggested based on the permeation of alcohols and the discharge of water and is supported by numerical calculations using a simple diffusion model. The effects of the CNT loading ratio and the as-prepared CAF diameter on the alcohol-dependent resistance change are investigated. Furthermore, the highly hydrated CAFs are used to determine the volume ratios of binary mixtures of methanol/ethanol and ethanol/water. Finally, we demonstrate that a CAF alcohol sensor can identify commercial liquors with different alcohol contents.