This composite hollow fiber membrane comprises a gas-permeable non-porous homogeneous layer which has a polyolefin resin (A) as the main component and a porous support layer which is made of a polyolefin resin (B) and which supports said non-porous homogeneous layer, and the composite hollow fiber membrane is characterized in that the polyolefin resin (A) of non-porous homogeneous layer is a block copolymer of ethylene units and at least one type of olefin unit selected from ±-olefin units having a carbon number of 3-20. By this means, a gas-permeable composite hollow fiber membrane is provided which has good gas permeability, reduces the impact of condensate on the performance of a gas dissolving module, and has excellent elution properties.