This paper presents a stochastic partial inventory model for the situation in which demand is deterministic, lead time follows normal distribution and backorder ratio during the stockout period decreases exponentially according to the length of backorder period. In this situation, an objective function is formulated to minimize the average annual cost, which is the sum of the ordering, carrying time-proportional backordering, quantity-proportional backordering and lost sales costs. And then the procedure of iterative solution method for the model is developed to find optimal reorder point and order quantity and numerical example to illustrate the proposed method is presented.