  We report the magnetic properties of newly synthesized, single crystals of
$\mathrm{TbTi_3Bi_4}$ whose crystal structure is highlighted by the stacking of
terbium-based zigzag chains and titanium-based kagome lattices. This compound
demonstrates extreme easy-axis magnetic anisotropy due to the
crystalline-electric-field effect which aligns the $\mathrm{Tb^{3+}}$ moments
along the zigzag chain direction. As the result of the strong single-ion
anisotropy and multiple magnetic interactions, $\mathrm{TbTi_3Bi_4}$ behaves as
a quasi-one-dimensional Ising magnet with a remarkable antiferromagnetic
ordering at $T_\mathrm{N}$ = 20.4 K. When a magnetic field is applied along the
direction of the zigzag chain, multiple meta-magnetic transitions occur between
1/3 and other magnetization plateaus. We have created a field-temperature phase
diagram and mapped out the complex magnetic structures resulting from
frustration.
