A mụrụ Smith na Septemba 25, 1968 na Philadelphia, Pennsylvania, nye Caroline (Bright), onye nchịkwa ụlọ akwụkwọ Philadelphia, na Willard Carroll Smith Sr., onye agha US Air Force na onye injinia refrigeration. Ọ tolitere na Wynnefield agbata obi West Philadelphia, ma zụlite Baptist. O nwere nwanne nwanyị tọrọ ya aha ya bụ Pamela na ụmụnne abụọ, ụmụ ejima Harry na Ellen. Smith gara Nwanyị Nwanyị Nwanyị nke Lourdes, ụlọ akwụkwọ elementrị Katọlik nkeonwe na Philadelphia. Ndị mụrụ ya kewara mgbe ọ dị afọ 13, mana ha agbaghị alụkwaghịm ruo ihe dị ka afọ 2000. Smith gara ụlọ akwụkwọ sekọndrị Overbrook. Ọ bụ ezie na a kọọrọ ya n'ọtụtụ ebe na Smith jụrụ inweta agụmakwụkwọ na Massachusetts Institute of Technology (MIT), ọ dịghị mgbe ọ tinyere akwụkwọ na kọleji n'ihi na ọ "chọrọ ịkwa iko".
Septemba 25, 1968