This paper presents a stochastic partial backorder inventory model for the situation in which demand follows normal distribution and back order ratio during that stockout period decreases exponentially according to the length of backorder period. In the paper, an objective function is formulated to minimize the average annual cost, which is the sum of the ordering, carrying, time-proportional backordering, and lost sales cost. And then sensitivity analysis for various exponential backorder ratios and standard deviations of leadtime demand are presented. The inventory model in the paper is reduced to a backorder model and lost sales model, when backorder ratio is 1 and 0, respectively.