Heavily obscured active galactic nuclei (AGNs) are known to show deep silicate absorption features in the mid-infrared (IR) wavelength range of 10--20~$mu$m. The detailed profiles of the features reflect the properties of silicate dust, which are likely to include information on AGN activities obscured by large amounts of dust. In order to reveal AGN activities obscured by large amounts of dust, we select 115 mid-IR spectra of heavily obscured AGNs observed by Spitzer/IRS, and systematically analyze the composition of silicate dust by spectral fitting using the 10~$mu$m amorphous and 23~$mu$m crystalline bands. We find that the main component of the silicate dust obscuring AGNs is amorphous olivine, the median mass column density of which is one order of magnitude higher than those of the minor components of amorphous pyroxene and crystalline forsterite. The median mass fraction of the amorphous pyroxene, $sim$2%, is significantly lower than that of the diffuse interstellar medium (ISM) dust in our Galaxy, while the median mass fraction of the crystalline forsterite, $sim$6%, is higher than that of the diffuse ISM dust. We also find that the mass fractions of the amorphous pyroxene and the crystalline forsterite positively correlate with each other. The low mass fraction of the amorphous pyroxene suggests that the obscuring silicate dust is newly formed, originating from starburst activities. The relatively high mass fraction of crystalline forsterite implies that the silicate dust is processed in the high temperature environment close to the nucleus and transported to outer cooler regions by molecular outflows. The positive correlation between the mass fractions can be naturally explained considering that amorphous pyroxene is transformed from crystalline forsterite by ion bombardments.