Very few researchers have considered inventory models with partial backlogging. The models developed earlier considered a fraction of demand to be backordered while the remaining fraction is lost during the stock out period. In this paper we have developed an inventory model with partial backlogging, redefining the demand rate at a particular instant as a function of the amount of orders already backlogged at that instant of time. Infinite replenishment rate and zero lead time are assumed. Expressions for optimum order quantity and optimuim value of maximum inventory are obtained by minimizing the total system costs. The model is illustrated with a numerical example, including sensitivity analysis with respect to the backlogging parameter.