Low-energy streams in peatlands often have a high sinuosity. However, it is unknown how this sinuous planform formed, since lateral migration of the channel is hindered by relatively erosion-resistant banks. We present a conceptual model of Holocene morphodynamic evolution of a stream in a peat-filled valley, based on a palaeohydrological reconstruction. Coring, ground-penetrating radar (GPR) data, and 14C and OSL dating were used for the reconstruction. We found that the stream planform is partly inherited from the Late-Glacial topography, reflecting stream morphology prior to peat growth in the valley. Most importantly, we show that aggrading streams in a peat-filled valley combine vertical aggradation with lateral displacement caused by attraction to the sandy valley sides, which are more erodible than the co-evally aggrading valley-fill. Owing to this oblique aggradation in combination with floodplain widening, the stream becomes stretched out as channel reaches may alternately aggrade along opposed valley sides, resulting in increased sinuosity over time. Hence, highly sinuous planforms can form in peat-filled valleys without the traditional morphodynamics of alluvial bed lateral migration. Improved understanding of the evolution of streams provides inspiration for stream restoration.