Inventory Control Problem is one of the problems in decision making and management that contains non-crisp parameters in real world. Economic Production Quantity (EPQ) model in fuzzy environment has been studied so far by many researchers. One of the main assumptions in all previous researches was neglecting the inventory shortage. In this research, a new multi-item EPQ model with fuzzy random demand allowing shortage and space constraint has been studied. In this model, the quantity of demand is employed using a trapezoidal fuzzy random number and the inventory shortage is considered as backorder The production and consumption are continuous throughout the period and the objective function is to minimize the total annual inventory costs. This is a non-linear objective function with a single constraint. To solve the model, the Lagrangian Relaxation method is used and using this method the space constraint is added to the objective function by a constant factor and the constraint is removed. To defuzzify the results the center of gravity method is used and finally to validate the model, a large numerical example (100 items) is provided.