In this paper analyzes fuzzy inventory system for deterioration item with time depended demand. Shortages are allowed under fully backlogged. Fixed cost, deterioration cost, shortages cost, holding cost are the cost considered in this model. Fuzziness is applying by allowing the cost components (holding cost, deterioration, shortage cost, holding cost, etc). In fuzzy environment it considered all required parameter to be triangular fuzzy numbers. One numerical solution of the model is obtained to verify optimal solution. The purpose of the model is to minimize total cost function.