The present invention relates to a new and distinct variety of grapevine, Vitis vinifera L., which will be denominated varietally as the ‘Sunpreme’ grapevine. The new and distinct ‘Sunpreme’ grapevine variety is characterized by the production of medium-sized green-colored seedless berries that begin to wilt naturally during mid-July in the San Joaquin Valley of Central California. The noted berry wilting is the first step in raisining, after which berries begin to brown naturally on the vine. The dried grapes (raisins) of this new variety are produced on strong woody canes that do not need to be cut from the mother vine to facilitate berry drying.