Production cross sections of iodine, tellurium and antimony radionuclides in the 24-59 MeV Li-7 + Sn-nat reaction have been measured by the conventional stacked foil technique with gamma-ray spectrometry. Excitation functions of the production cross sections were compared with a statistical model calculation, indicating complete and incomplete fusion reactions produce the radionuclides. The integral yields of I-123,I-124,I-125,I-126 were deduced from the calculated excitation functions in the Li-7 induced reactions on Sn-nat, Sn-122 Sn-120 and Sn-119 in view of the production of medically important I-123,I-124 and radionuclidic impurities of long-lived I-125,I-126. The results are discussed by comparing with literature values obtained with other reactions.