Sainsbury’s has begun work on a store on the site of a former college in Liverpool Road, Newcastle-under-Lyme.
Neighbours said their homes and gardens were being covered by dust.
The firm said it was trying to reduce the dust by damping down roads and dust piles on the site but it had not ruled out compensation for some residents.
Ben Proctor, who lives near the site, said: “Sainsbury’s knocked the college down and they are recycling all the stone.
“It’s going through a crusher and sending up a large amount of dust that blows all over the properties. It’s terrible it covers all the plants, the shed, it covers your whole yard. It just looks terrible and it’s just not on really.”
A spokesman for the company said: “We’ve really been doing all we can to try and stop the dust getting into the air. Read more….