In this paper a framework for a new heuristic approach for solving the single level multi-item capacitated dynamic lot sizing problem is presented. The approach uses an iterative item-by-item strategy for generating solutions to the problem. In each iteration a set of items are scheduled over the planning horizon and the procedure terminates when all items are scheduled. An algorithm that implements this approach is developed in which in each iteration a single item is selected and scheduled over the planning horizon. Each item is scheduled by the solution of a bounded single item lot sizing problem where bounds on inventory and production levels are used to ensure feasibility of the overall problem. The performance of this algorithm is compared to some well-known heuristics over a set of test problems. The computational results demonstrated that on the average our algorithm outperforms other algorithms. The suggested algorithm especially appears to outperform other algorithm for problems with many periods and few items. In the literature these problems are considered as hard.