For a fiber optical surface plasmon resonance (SPR) sensor a short part of its cladding should be removed to coat a thin layer of a metal. Usually this is problematic when an optical fiber with small core diameter is used. In this paper, a new method using µliter droplet of the HF acid for short fiber optical taper fabrication is reported. Using this method in a multi-mode optical fiber with the core/cladding size of 50/125 µm a 2 mm long taper with 40 µm diameter is fabricated. Roughness of its surface is investigated using an atomic force microscopy. The measured mean value of the roughness is about 8 nm. A 60 nm thin layer of pure silver is coated on the taper surface in order to investigate its performance using a fiber optical SPR sensor.  Using this SPR fiber sensor measurement of the lead concentrations in water ranging from 0.1 to 10 part per million (ppm) is reported.