Single Valued Neutrosophic Numbers in numerous forms are useful tool for dealing with indeterminate and inconsistent information encountered in real world. At times more emphasis have to be given to the indeterminate information and in such case these concepts may not be sufficient to deal with it. To overcome this, in this paper we have proposed the definition of Gaussian Double Refined Indeterminate Neutrosophic Number (GDRINN).Also we developed a ranking method based on the α - cut and is applied to the decision making algorithm. The method is exhibited with a hypothetical case study