We report a direct measurement of the imaginary part of the surface tension of water through a dynamic scheme using a thin vertical glass fiber of diameter of 3 μm with one end glued onto a cantilever beam and the other end touching a water-air interface. The frequency dependence of the dissipation factor experienced by the glass fiber is exactly calculated through measuring the phase delay with various frequencies when the glass fiber is forced to oscillate vertically. We find the same intercept at the dissipation factor axis for different frequency dependences of the dissipation factor for different depths by which the glass fiber is dipped into water. This nonzero dissipation factor at zero frequency presents direct evidence of the existence of the imaginary part of surface tension of water and yields a complex surface tension of water σ^∗=0.073 + i(0.017 ± 0.002) N/m at room temperature.