Disclosed is a new variety of Prunus persica named ‘SMOOTH TEXAN THREE’. This new variety, which requires approximately 650 chilling units of dormancy, is considered to be a nectarine tree of early mid-season maturity, which ripens in late May to early June in the medium chill zone of Texas and which produces yellow fleshed fruit that are firm, attractively colored, with excellent sub-acid flavor and suitable for both local and regional markets.