One of the most disturbing issues of third world countries in general and Nigeria in particular is the challenge of poverty eradication. The poverty situation in Nigeria has steadily grown in magnitude in recent times despite various programmes proffered towards alleviating poverty in the country. But unfortunately, in formulating and implementing these programmes, not much attention has been accorded education as an effective tool for poverty reduction. This paper, therefore, examined poverty situation and the possibility of achieving sustainable poverty reduction in Nigeria through quality education. Through a descriptive and historical analysis of documentary data, the paper argued that the various poverty alleviation programmes and strategies adopted in Nigeria are mere remedial measures to cushion the effects of poverty and therefore cannot actually eradicate poverty in the country. Conclusively, the paper emphasized the adoption of a new approach to poverty alleviation through massive and quality education for all. This the government can do by making education affordable and accessible to the poor and their children.