Food insecurity is a term used to measure hunger and food deprivation of a large population. As per the 2015 statistics provided by Feeding America - one of the largest domestic hunger-relief organizations in the United States, 42.2 million Americans live in food insecure households, including 29.1 million adults and 13.1 million children. This constitutes about 13.1% of households that are food insecure. Food Banks have been developed to improve food security for the needy. We have developed a novel food distribution policy using suitable welfare and poverty indices and functions. In this work, we propose an equitable and fair distribution of donated foods as per the demands and requirements of the people, thus ensuring minimum wastage of food (perishable and non-perishable) with focus towards nutrition. We present results and analysis based on the application of the proposed policy using the information of a local food bank as a case study. The results show that the new policy performs better than the current methods in terms of population being covered and reduction of food wastage obtaining suitable levels of nutrition.