The beach has been cordoned off with red and white tape to stop individuals harassing the mammal, which has taken up residence on the stoney beach between The Spyglass Inn and the Harbour.
Grumpy is thought to be well but is of older years – possibly over 30-years-old. He is known to experts locally and left West Sussex on Wednesday.
Those visiting the area should keep their distance by observing from the Esplanade. Dogs should be kept on leads and away from the seal.