In this paper, most of the researchers have assumed that shortages are completely backlogged or completely lost. Consequently, the opportunity cost due to lost sales should be considered in the modeling. In the present work an inventory model is developed and analyzed with partial backlogging. The backlogging rate is taken to be inversely proportional to the waiting time for the next replenishment. Deterioration rate is taken as time dependent and concept of life time is taken in consideration, which is a realistic situation for the fresh and new items in stock.