Thermal conductivity measurements have been carried out for single crystals of the one-dimensional (1D) antiferromagnetic (AF) Ising-like spin system ACoX3 (A = Rb, Cs; X = Cl, Br). A shoulder originating from the thermal conductivity due to spin excitations, -κ spin , has been observed around 60K in the temperature dependence of the thermal conductivity along the c-axis parallel to spin chains for every ACoX3. To our knowledge, this is the first observation of -κ spin in 1D AF Ising-like spin systems. It has been found that the magnitude of -κ spin in ACoX3 is a little smaller than those in 1D AF Heisenberg spin systems. The reason is discussed in terms of the Heisenberg-like character in ACoX3.