A support structure of a heat-pipe multi-layer wick structure, having a hollow heat-pipe tube and multiple separate layers of weaving mesh wick structure overlaying on an interior surface of the heat-pipe tube. The wick structure has a curly circular shape. The outermost layer of the wick structure has lower melting point compared to the inner layers of thereof. Thereby, the capillary force of the heat pipe is enhanced, while the mesh at the inner layers with higher melting point provides better support to the outer layers of the wick structure.