We report a three-dimensional (3D) SERS substrate consisting of a silver nanoparticle (AgNP) coating on the skeleton-fiber surfaces of a polytetrafluoroethylene (PTFE) membrane. Simple thermal evaporation was employed to deposit Ag onto the PTFE membrane to produce grape-shaped AgNPs. The 3D-distributed AgNPs exhibit not only strong localized surface plasmon resonance (LSPR) but also strong hydrophobic performance. High-density hotspots via silver nano-grape structures and nanogaps, the large 3D interaction volume, and the large total surface area, in combination with the hydrophobic enrichment of the specimen, facilitate high-sensitivity sensing performance of such a SERS substrate for the direct detection of low-concentration molecules in water. An enhancement factor of up to 1.97 × 1010 was achieved in the direct detection of R6G molecules in water with a concentration of 10−13 mol/L. The lowest detection limit of 100 ppt was reached in the detection of melamine in water. Such a SERS sensor may have potential applications in food-safety control, environmental water pollution monitoring, and biomedical analysis.