A fluid viscosity sensor using bend loss theory is presented. The sensing principle makes use of the damping characteristic of a vibrating optical fiber probe with fix-free end configuration. By measuring the frequency response of the fiber probe, the viscosity can be determined from the displacement of the fiber. The physical and mathematical model of the vibrating fiber submerged in a viscous fluid has been put forward. The impact of the viscosity and density on the resonance frequency shift has been elucidated. Based on the solution of the model methods of the viscosity extraction from maximum vibrational amplitude and bandwidth have been proposed.