RNA N6-methyladenosine (m6A) modifications are essential in plants. Here, we show that transgenic expression of the human RNA demethylase FTO in rice caused a more than threefold increase in grain yield under greenhouse conditions. In field trials, transgenic expression of FTO in rice and potato caused ~50% increases in yield and biomass. We demonstrate that the presence of FTO stimulates root meristem cell proliferation and tiller bud formation and promotes photosynthetic efficiency and drought tolerance but has no effect on mature cell size, shoot meristem cell proliferation, root diameter, plant height or ploidy. FTO mediates substantial m6A demethylation (around 7% of demethylation in poly(A) RNA and around 35% decrease of m6A in non-ribosomal nuclear RNA) in plant RNA, inducing chromatin openness and transcriptional activation. Therefore, modulation of plant RNA m6A methylation is a promising strategy to dramatically improve plant growth and crop yield.