A police spokeswoman said the search was concentrating on Motutaiko Island after the discovery of the wetsuit and one theory was that Mr Grant might be on the island. The island is about 3.4km from the shore and covers an area of about 11ha.
She said police were appealing for anyone who had seen a swimmer near the island on Friday evening or any boaties who had been approached for a ride or taken someone to or from, the island to contact them.
A team of 25 Land Search and Rescue volunteers and police are searching the island and the waters surrounding it and police are working with iwi representatives because the island has areas which are wahi tapu (sacred places).
Anyone with information should contact Taupo Police on 07 378 6060.