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A company may have backorders if they run out of the stock in their stores, in which case, it can just place a new order to restock its shelves. A customer who is willing to wait for some time until the company has restocked the products would have to place a backorder. A backorder only exists if customers are willing to wait for the order. In this paper, a neutrosophic inventory backorder problem using a triangular neutrosophic numbers is introduced. First, we fuzzify the carrying cost and shortage cost as triangular neutrosophic numbers and the signed distance method is used to defuzzify them. From these, we can obtain the neutrosophic optimal shortage quantity and the neutrosophic total cost. A numerical example is provided to illustrate the proposed model in neutrosophic environment.