Quality Function Deployment (QFD) method, is one of the developed method in Engineering Quality which through studying marketing, identifying requirements and commitments of customers and identifying technical and Engineering characteristics, tries to consider that in all processes of development and manufacturing for new product development (NPD), function in direction of increasing marketing share and customer satisfaction one of the important steps in QFD method, determining quantitative amounts of HOQ. Nowadays, regarding the increase of complexity and uncertainty of information, evaluating and decision-making to determine quantity of HOQ as an absolute number is a complex issue. In the previous studies conducted, Fuzzy logic was used for determining numerical quantity of HOQ for the conditions where the decision-maker was faced verbal or vague information. However, since information in the real world is insufficient or incomplete, one can use Grey Numbers in the form of an interval instead of absolute or Fuzzy numbers to determine the credit for each indicator so that, besides avoiding modeling for fuzzy numbers or error-accepting in absolute models, the simplicity of grey numbers is practiced. In present study it is deal with presenting Linear Goal Programming Method in grey conditions. First, because of insufficiency and incompleteness of information in the present field of grey numbers theory, Quality Function Deployment method is used. Also, to determine the relative importance, the weighting in Linear Goal Programming Method based on grey numbers is used, with regard to the results gained from the model, one can claim that the presented model can be used where the Quality Function Deployment Method can give incomplete, vague information. The validity of the proposed method is measured in the form of a case study which investigates the customer satisfaction regarding Iranian olive oil quality.