Abstract: An inventory model is developed for deteriorating items during stock-out which is partial backlogging. In the earlier researches on inventory of deteriorating items, the unsatisfied demand was usually assumed that it is completely due to backlog, and the purchase cost and the cost of lost sales were ignored in calculating the total cost, thus resulting in a big gap between the inventory model and reality. The backlogging rate of unsatisfied demand linearly depending on the total number of customers in the waiting line is used to present the condition during stock-out and both the purchase cost and the cost of lost sales are included in the total cost, then an optimal inventory model is developed by extending the constant demand function of goods into time-varying concave demand function. A simple algorithm is also provided to find the optimal ordering policy for this model. Further, a numerical example is given to illustrate the results.