Disclosed is a new nectarine variety of Prunus persica named ‘SMOOTH ZEST ONE’. This new variety, which requires 200-250 chilling units of dormancy, is considered to be a nectarine tree of early season maturity, which ripens in early to mid May in the medium chill zone of Texas and produces white fleshed fruit that are firm, attractively colored, and suitable for both local and regional fresh fruit markets.