A new and distinct peach variety of Prunus persica named `NJ351` is provided. This variety is distinguished from other peach varieties by its unique combination of nonshowy flowers, fruit that ripen in late-midseason, attractively blushed fruit with a bright golden-yellow ground color, freestone fruit with a juicy, nearly nonmelting texture and sweet, low acid flavor, firm fruit that retain their firmness well and trees with regular, heavy production of fruit.