Food security is recognized as a basic human right and in the ‘Sustainable Development Summit’ of 2015, achieving ‘Zero Hunger’ by 2030 has been set as one of the 17 sustainable development goals. The incidence of hunger is very much region or context-specific. India remains at ‘serious’ category in Global Hunger Index Severity Scale, 2017. Food accessibility being the most important pillar of food security, in this paper we attempt to assess the incidence, depth and severity of food inaccessibility at the household level in three villages of the district of Birbhum, West Bengal. The study, based on primary data covering 257 households, also intends to examine food accessibility of the households classified by their primary source of income. We have taken monthly per capita consumption expenditure (MPCE) on food as the indicator of food accessibility. The MPCE on food as per the minimum food basket set by the Planning Commission in 2014 and the mean MPCE on food for rural West Bengal as determined by the NSSO in 2011 are considered as two threshold levels. The study reveals the alarming reality that a significant percentage of households with zero operational land and marginal farmers do not have food accessibility. An inquiry into the sources of income of the households reveals that there exists (i) a negative relation between wage income and food accessibility, (ii) an inverse relation between income generated from farm activity and food accessibility and (iii) a positive relation between income from regular service, trade, business and food accessibility.