The recently developed Nambu-Jona-Lasinio (NJL) -jet model is used as an effective chiral quark theory to calculate the quark fragmentation functions to pions, kaons, nucleons, and antinucleons. The effects of the vector mesons ρ, K * , and φ on the production of secondary pions and kaons are included. The fragmentation processes to nucleons and antinucleons are described by using the quark-diquark picture, which has been shown to give a reasonable description of quark distribution functions. We incorporate effects of next-to-leading order in the Q 2 evolution, and compare our results with the empirical fragmentation functions.