The aim of this paper is to price an American option in a multiperiod binomial model,when there is uncertainty on the volatility of the underlying asset.American option valuation is usually performed, under the risk-neutralvaluation paradigm, by using numerical procedures such as the binomialoption pricing model of Cox, Ross, Rubinstein (1979). A key input of themultiperiod binomial model is the volatility of the underlying asset,that is an unobservable parameter.As it is hard to give a precise estimate forthe volatility, in this paper we use a possibility distribution in order to modelthe uncertainty on the volatility. Possibility distributions are one of the mostpopular mathematical tools for modelling uncertainty. The standard risk-neutralvaluation paradigm requires the derivation of the risk-neutral probabilities, thatin a one period binomial model boils down to the solution of a linear system ofequations. As a consequence of the uncertainty in the volatility, we obtain apossibility distribution on the risk-neutral probabilities. Under these measures,we perform the risk-neutral valuation of the American option.