We consider discrete time hedging error of the American put option in case of brusque fluctuations in the price of assets. Since continuous time hedging is not possible in practice so we consider discrete time hedging process. We show that if the proportions of jump sizes in the asset price are identically distributed independent random variables having finite moments then the value process of the discrete time hedging uniformly approximates the value process of the corresponding continuous-time hedging in the sense of L1 and L2-norms under the real world probability measure.