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In this paper, the optimization of a fuzzy inventory model under fuzzy demand is done. Due to uncertainty in demand, we can express it using some fuzzy distribution which depends on the inventory manager. The fuzzy demand leads to a fuzzy total cost function of the inventory problem. The paper uses three types of fuzzy numbers to represent the uncertain demand and the expected value of the total cost function is minimized so as to find the optimal value of order quantity using each. The expected value of the total cost function is based on the lambda pessimistic and optimistic values of the fuzzy variables. The formulae for optimal order quantity are then derived. The results are justified with the help of some numerical illustrations. The methodology of the paper can also be applied to other inventory problems under uncertain factors affecting the total cost of the problem.Keywords: Fuzzy Inventory·Order Quantity·Fuzzy variable·L-R type fuzzy number·Fuzzy expectation·Optimal order quantity·lambda pessimistic value·Lambda optimistic value