In this study, a deterministic inventory model has been developed for which items are subject to linear deterioration. Here shortages are allowed and are partially backlogged. The unsatisfied demand is backlogged and is a function of time. We have established the optimal order quantity by minimizing the total inventory cost. To illustrate the model a numerical example has been provided and also Sensitivity analysis has been carried out to study the effect of parameters on decision variables and the total cost of an inventory of this model.