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The mechanism of thermal conductivity in amorphous polymers,especially polymer fibers,is unclear in comparison with that in inorganic materials.Here,we report the observation of a crossover of heat conduction behavior from three dimensions to quasi-one dimension in polyimide nanofibers at a given temperature.A theoretical model based on the random walk theory has been proposed to quantitatively describe the interplay between the inter-chain hopping and the intra-chain hopping in nanofibers.This model explains well the diameter dependence of thermal conductivity and also speculates on the upper limit of thermal conductivity of amorphous polymers in the quasi-1D limit.