Ged Parker has submitted the application for the dwelling at Maythorn near the wind farm Crowedge.
Mr Parker and his wife wish to build a three-bedroom home that is completely covered in earth and grass – to enable sheep to graze on it.
The home would be warmed by geo-thermal heat and electricity would be produced from the heat of the earth and solar power.
Mr Parker said: "It may sound bizarre but it makes total and complete sense and even though it is high on the hills, no one will be able to see the house because of it being mostly covered with earth – unless they are flying over it."
Planning officials have told Sheffield Today that the plans are "unique" and that the dwelling could fit into the "very special circumstances" needed for planning permission in the moorlands of the Pennines.