  We study the ground-state phase diagram of the $S=1$ bilinear-biquadratic
model\,(BLBQ) on the star lattice with the state-of-art tensor network
algorithms. The system has five phases: the ferromagnetic, anti-ferromagnetic,
ferroquadrupolar, and spin-liquid phases. The phases and their phase boundaries
are determined by examining various local observables, correlation functions
and transfer matrices exhaustively. The spin liquid phase, which is the first
quantum disordered phase found in two-dimensional BLBQ model, is gapped and
devoid of any conventional long-range order. It is also characterized by
fixed-parity virtual bonds in the tensor network formalism, analogous to the
Haldane phase, while the parity varies depending on the location of the bond.
