One main theme in current condensed matter physics is the search of quantum spin liquid (QSL), an exotic magnetic state with strongly-fluctuating and highly-entangled spins down to zero temperature without static order. However, there is no consensus on the existence of a QSL ground state in any real material so far. The disorders and competing exchange interactions may prevent the formation of an ideal QSL state on frustrated spin lattices. Here we report systematic heat transport measurements on a honeycomb-lattice compound BaCo2(AsO4)2, which manifests magnetic order in zero field. In a narrow field range after the magnetic order is nearly suppressed by an in-plane field, in both perpendicular and parallel to the zigzag direction, a finite residual linear term of thermal conductivity is clearly observed, which is attributed to the mobile fractionalized spinon excitations. This provides smoking-gun evidence for a gapless QSL state in BaCo2(AsO4)2. We discuss the underlying physics to form this exotic gapless QSL state in Co2+ honeycomb lattice.