The owners of a cottage on Catholic Lane, in Sedgley, applied to build the garage next to the two-storey building, which was won last year as part of a competition alongside a £50,000 Range Rover.
The cottage is located in an area in Sedgley which overlooks Cotwell End Local Nature Reserve. House prices on the Lane regularly top £500,000.
The application said that the two-storey cottage appears on historical maps dating back to 1826 and is locally listed.
It read: "It is proposed to construct a detached 6 Car Garage to the rear of the existing property, making use of the existing fall of the site to ensure the continued uninterrupted views for both the occupant and their neighbours.
"The garage will not be visible from the public highway."
No neighbours were reported to have objected, but planners at Dudley Council turned down the application on February 1, saying that the impact on the area would be detrimental to the amenity, character and appearance.
The note from the planners read: "The proposed development due to its design, prominence through excessive rearward projection and impact upon outlook would be a discordant and incongruous addition that does not relate to the existing dwelling.
"It would result in a detrimental impact upon the amenity, character and appearance of the surrounding area."