  The Kitaev-type spin chains have been demonstrated to be fertile playgrounds
in which exotic phases and unconventional phase transitions are ready to
appear. In this work, we use the density-matrix renormalization group method to
study the quantum phase diagram of a spin-1 Kitaev chain with a tunable
negative single-ion anisotropy (SIA). When the strength of the SIA is small,
the ground state is revealed to be a spin-nematic phase which escapes
conventional magnetic order but is characterized by a finite spin-nematic
correlation because of the breaking spin-rotational symmetry. As the SIA
increases, the spin-nematic phase is taken over by either a dimerized phase or
an antiferromagnetic phase through an Ising-type phase transition, depending on
the direction of the easy axis. For large enough SIA, the dimerized phase and
the antiferromagnetic phase undergo a ``Landau-forbidden" continuous phase
transition, suggesting new platform of deconfined quantum critical point in
spin-1 Kitaev chain.
