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By 2030, the average cost of key crops could increase by between 120% and 180%, the charity forecasts.
It is the acceleration of a trend which has already seen food prices double in the last 20 years.
Half of the rise to come will be caused by climate change, Oxfam predicts.
It calls on world leaders to improve regulation of food markets and invest in a global climate fund.
"The food system must be overhauled if we are to overcome the increasingly pressing challenges of climate change, spiralling food prices and the scarcity of land, water and energy," said Barbara Stocking, Oxfam's chief executive. Women and children
World food prices have already more than doubled since 1990, according to Food and Agricultural Organization (FAO) figures, and Oxfam predicts that this trend will accelerate over the next 20 years.
In its report, Growing a Better Future, Oxfam says predictions suggest the world's population will reach 9bn by 2050 but the average growth rate in agricultural yields has almost halved since 1990.