A new and distinct peach variety of Prunus persica named ‘NJ355’ is provided. This variety is distinguished from other peach varieties by its unique combination of non-showy flowers, fruit that ripen in early-season with an attractive red and greyed-purple over color and orange-white ground color, clingstone fruit with a juicy, firm nonmelting texture and sweet, slightly acidic flavor, and excellent production of firm fruit that maintain their eating quality following cold storage.