An haifi Smith a ranar 25 ga Satumba, 1968 a Philadelphia, Pennsylvania, zuwa Caroline (Bright), mai kula da hukumar makarantar Philadelphia, da Willard Carroll Smith Sr., tsohon soja na Sojan Sama na Amurka da injiniyan firiji. Ya girma a unguwar Wynnefield na Yammacin Philadelphia, kuma an tashe shi Baptist. Yana da wata 'yar'uwa babba mai suna Pamela da ƙananan' yan'uwa biyu, tagwaye Harry da Ellen. Smith ya halarci Our Lady of Lourdes, makarantar firamare ta Katolika mai zaman kanta a Philadelphia. Iyayensa sun rabu lokacin da yake 13, amma ba su saki ba har zuwa 2000. Smith ya halarci makarantar sakandare na Overbrook.
25 ga Satumba, 1968