  Frustration in quantum spin systems promote a variety of novel quantum
phases. An important example is the frustrated spin-$1$ model on the square
lattice with the nearest-neighbor bilinear ($J_1$) and biquadratic ($K_1$)
interactions. We provide strong evidence for a nematic spin liquid phase in a
range of $K_1/J_1$ near the SU(3)-symmetric point ($J_1 = K_1$), based on the
linear flavor-wave theory and extensive density matrix renormalization group
calculation. This phase displays no spin dipolar or quadrupolar order,
preserves translational symmetry but spontaneously breaks $C_4$ lattice
rotational symmetry, and possesses fluctuations peaked at the wavevector $(\pi,
2\pi/3)$. The spin excitation gap drops rapidly with system size and appears to
be gapless, and the nematic order is attributed to the dominant $(\pi, 2\pi/3)$
fluctuations. Our results provide a novel mechanism for electronic nematic
order and, more generally, open up a new avenue to explore frustration-induced
exotic ground states.
