  Low-dimensional magnetic materials have attracted much attention due to their
novel properties and high potential for spintronic applications. In this work,
we study the electronic structure and magnetic properties of the pseudo
one-dimensional compound CrSbSe$_3$, using density functional calculations,
superexchange model analyses, and Monte Carlo simulations. We find that
CrSbSe$_3$ is a ferromagnetic (FM) semiconductor with a band gap of about 0.65
eV. The FM couplings within each zig-zag spin chain are due to the Cr-Se-Cr
superexchange with the near-90$^\circ$ bonds, and the inter-chain FM couplings
are one order of magnitude weaker. By inclusion of the spin-orbit coupling
(SOC) effects, our calculations reproduce the experimental observation of the
easy magnetization $a$ axis and the hard $b$ axis (the spin-chain direction),
with the calculated moderate magnetic anisotropy of 0.19 meV/Cr. Moreover, we
identify the nearly equal contributions from the single ion anisotropy of Cr,
and from the exchange anisotropy due to the strong SOC of the heavy elements Sb
and Se and their couplings with Cr. Using the parameters of the magnetic
coupling and anisotropy from the above calculations, our Monte Carlo
simulations yield the Curie temperature $T_{\rm{C}}$ of 108 K.
