This striking portrait of the young Baptist would appear to accord with the works of Lorenzo Lippi of the 1630's.  During this time the artist produced a few such bust paintings of saints, the closest comparison to the present work being a Head of Saint John the Baptist in a private collection, Florence (see C. d'Afflitto, Lorenzo Lippi, Florence 2002, pp.56-57, 207, cat. no. 36, illus., in color, p. 57).  That painting is inscribed on the reverse "25 9bre 1638," thus suggesting a date for the picture, or at least a terminus ante quem. Both paintings depict the saint as a young man, rosy cheeked and lipped, holding a reed cross made in the same manner.