  We employ Monte Carlo simulations in order to investigate critical behavior
of a geometrically frustrated spin-1 Ising antiferromagnet on a triangular
lattice in the presence of a single-ion anisotropy. It has been previously
found that long-range order can exist in the isotropic system with a spin
larger than some critical value estimated as 11/2. We show that the presence of
the single-ion anisotropy can lead to a partial long-range order in the
low-temperature region even below this critical value, namely for the spin 1,
within a certain range of the anisotropy strength. At higher temperatures we
identify another phase of the Berezinsky-Kosterlitz-Thouless type and using a
finite-size scaling analysis evaluate the correlation decay exponent. We also
study densities of various local spin patterns in the respective phases.
