AbstractTropical peatlands are a known source of methane (CH4) to the atmosphere, but their contribution to atmospheric CH4 is poorly constrained. Since the 1980s, extensive areas of the peatlands in Southeast Asia have experienced land‐cover change to smallholder agriculture and forest plantations. This land‐cover change generally involves lowering of groundwater level (GWL), as well as modification of vegetation type, both of which potentially influence CH4 emissions. We measured CH4 exchanges at the landscape scale using eddy covariance towers over two land‐cover types in tropical peatland in Sumatra, Indonesia: (a) a natural forest and (b) an Acacia crassicarpa plantation. Annual CH4 exchanges over the natural forest (9.1 ± 0.9 g CH4 m−2 year−1) were around twice as high as those of the Acacia plantation (4.7 ± 1.5 g CH4 m−2 year−1). Results highlight that tropical peatlands are significant CH4 sources, and probably have a greater impact on global atmospheric CH4 concentrations than previously thought. Observations showed a clear diurnal variation in CH4 exchange over the natural forest where the GWL was higher than 40 cm below the ground surface. The diurnal variation in CH4 exchanges was strongly correlated with associated changes in the canopy conductance to water vapor, photosynthetic photon flux density, vapor pressure deficit, and air temperature. The absence of a comparable diurnal pattern in CH4 exchange over the Acacia plantation may be the result of the GWL being consistently below the root zone. Our results, which are among the first eddy covariance CH4 exchange data reported for any tropical peatland, should help to reduce the uncertainty in the estimation of CH4 emissions from a globally important ecosystem, provide a more complete estimate of the impact of land‐cover change on tropical peat, and develop science‐based peatland management practices that help to minimize greenhouse gas emissions.