The prime objective of this paper is to quantitatively estimate seismic attenuation caused by fractures with different physical parameters. In seismic wave simulation, the fractured media are treated as the anisotropic media and fractures are represented by frequency-dependent elastic constants. Based on numerical experiments with three different parameters, namely viscosity, porosity and the Lamé parameters, this paper has the following observations. First, seismic attenuation is not affected by the viscosity within fractures, although it increases with the increase of porosity and decreases with the increase of the Lamé parameters within fractures. Among the latter two parameters, seismic attenuation is more sensitive to the Lamé parameters than to the porosity. Second, for the attenuation anisotropy, low frequencies have more anisotropic effect than high frequencies. For example, a 50 Hz wavefield has the strongest anisotropy effect if compared to 100 and 150 Hz wavefields. The attenuation anisotropy for low frequency (say 50 Hz) is more sensitive to the viscosity than the porosity and the Lamé parameters have the weakest effect among these three parameters. These observations suggest that low-frequency seismic attenuation, and especially the attenuation anisotropy in low frequency, would have great potential for fluid discrimination within fractured media.