The reaction between iodate and thiourea has been studied in an unbuffered acidic medium. In excess iodate the reaction shows not only oligooscillations in pH, Pt potential and the concentration of iodide ion, [I-], but also an initial induction period which has the linear relation with initial pH. At the end of the induction period, [I-] decreases sharply and a yellow coloration (due to iodine) appears transiently. While in excess thiourea iodine is produced and finally consumed, leaving milky deposits (due to sulfur) at the end of the reaction. The induction period from the start of the reaction to the maximum of [I2] is also directly proportional to initial pH. A 14-step mechanism, including a H+-mediated preequalibrium, Dusman reaction, iodine-sulfur reactions and sulfur-sulfur reactions, is proposed. Computer simulations using this mechanism give good agreement with experiments.