Acoustic insulation structure for a power train, comprising: a cover member (40; 64) that is adapted to cover at least an internal combustion engine of the power train including the internal combustion engine and that includes a pool portion (40a; 64a) in which water that has entered into an inside of the cover member (40; 64) pools, wherein the cover member (40; 64) is configured by a double structure with a material having a high acoustic performance on the outside; and a water-absorption member (42; 66) that is arranged at the inside of the cover member (40; 64) and configured by a material that is softer than that of the cover member (40; 64), wherein: the cover member and the water-absorption member are adapted to be attached to the internal combustion engine such that the cover member is adapted to cover a lower portion of the internal combustion engine including a bottom portion of the internal combustion engine with the pool portion being arranged at a location opposed to the bottom portion, the cover member (40; 64) includes a moisture outlet (44, 46) that is adapted to release, into an atmospheric air, moisture present inside the cover member (40; 64), the water-absorption member (42; 66) extends from the pool portion (40a; 64a) to the moisture outlet (44, 46), and a surface of the cover member is subjected to water-repellent treatment. a cover member (40; 64) that is adapted to cover at least an internal combustion engine of the power train including the internal combustion engine and that includes a pool portion (40a; 64a) in which water that has entered into an inside of the cover member (40; 64) pools, wherein the cover member (40; 64) is configured by a double structure with a material having a high acoustic performance on the outside; and a water-absorption member (42; 66) that is arranged at the inside of the cover member (40; 64) and configured by a material that is softer than that of the cover member (40; 64), wherein: the cover member and the water-absorption member are adapted to be attached to the internal combustion engine such that the cover member is adapted to cover a lower portion of the internal combustion engine including a bottom portion of the internal combustion engine with the pool portion being arranged at a location opposed to the bottom portion, the cover member (40; 64) includes a moisture outlet (44, 46) that is adapted to release, into an atmospheric air, moisture present inside the cover member (40; 64), the water-absorption member (42; 66) extends from the pool portion (40a; 64a) to the moisture outlet (44, 46), and a surface of the cover member is subjected to water-repellent treatment. the cover member and the water-absorption member are adapted to be attached to the internal combustion engine such that the cover member is adapted to cover a lower portion of the internal combustion engine including a bottom portion of the internal combustion engine with the pool portion being arranged at a location opposed to the bottom portion, the cover member (40; 64) includes a moisture outlet (44, 46) that is adapted to release, into an atmospheric air, moisture present inside the cover member (40; 64), the water-absorption member (42; 66) extends from the pool portion (40a; 64a) to the moisture outlet (44, 46), and a surface of the cover member is subjected to water-repellent treatment.