The study employed multinomial logit and fractional regression models to investigate determinants of food-poverty FP states and the demand for dietary diversity, respectively using 2003/2004 Nigerian Living Standard Survey (NLSS) data. The FP states is derive by combining two food security indicators defined as food expenditure (FOOD_exp) and dietary diversity score (DDS), which yielded four possible scenarios viz. completely food secure, food insecure based on FOOD_exp only, food insecure based on DDS only, and completely food insecure households in the study. The determinants of the household FP states show that odds ratio of households being in state of food insecure relative to completely food secure increased significantly with household size, among households headed by farmers, households that own produced and purchase only food consumed, and households in the rural areas but decrease significantly as income level increases. Also, the determinants of household dietary diversity shows that household income, household size, household with members <40 years old, households headed by farmers and households in rural areas, increased significantly dietary diversity consumed in the study. In contrast, more educated household head and household that only home produced their food are likely to demand for less dietary diversity. The implication of these findings is that households in the different states of food-poverty problem are likely to be affected by different socio-economic characteristics, as demand for dietary diversity also differ across household socio-economic variables in Nigeria. Based on this, the study suggests that the present approach could be useful in targeting different types of food insecurity problem in the developing economies and Nigeria as a whole.