In this paper an inventory model is presented for determining the ordering schedule in which the demand rate is changing linearly with time and the decay is assumed to be a constant rate of the on-hand inventory. An easy to use heuristic is developed to find the times and sizes of replenishments so as to keep the total of ordering, inventory carrying and deteriorating costs as low as possible. Solutions of the model to test problems show that our heuristic model outperforms other existing models in the literature without sacrificing the computational complexity. When there is no deterioration, the model developed is related to the corresponding model of nondeteriorating items.