A continuous production control inventory model for deteriorating items with variable demand rate is developed. Demand rate is the linear function of time. In this paper we have done all work in the environment of permissible delay of payments. A number of structural properties of the inventory system are studied analytically. We have discussed the minimum total system cost under the condition of permissible delay is relaxed to that at the end of the credit period, the retailer will make a partial payment on total purchasing cost to the supplier and pay off the remaining balance by loan from the bank. Numerical examples are taken to illustrate the procedure of finding the optimal total inventory cost and production cycle time. Sensitivity analysis is carried out to demonstrate the effects of changing parameter values on the optimal solution of the system.