  The process $e^{+}e^{-}\rightarrow D_{s}^{\ast+}D_{s}^{\ast-}$ is studied
with a semi-inclusive method using data samples at center-of-mass energies from
threshold to 4.95 GeV collected with the BESIII detector operating at the
Beijing Electron Positron Collider. The Born cross sections of the process are
measured for the first time with high precision in this energy region. Two
resonance structures are observed in the energy-dependent cross sections around
4.2 and 4.4 GeV. By fitting the cross sections with a coherent sum of three
Breit-Wigner amplitudes and one phase-space amplitude, the two significant
structures are assigned masses of (4186.5$\pm$9.0$\pm$30) MeV/$c^{2}$ and
(4414.5$\pm$3.2$\pm$6.0) MeV/$c^{2}$, widths of (55$\pm$17$\pm$53) MeV and
(122.6$\pm$7.0$\pm$8.2) MeV, where the first errors are statistical and the
second ones are systematic. The inclusion of a third Breit-Wigner amplitude is
necessary to describe a structure around 4.79 GeV.
