  Spin squeezing, as a crucial quantum resource, plays a pivotal role in
quantum metrology, enabling us to achieve high-precision parameter estimation
schemes. Here we investigate the spin squeezing and the quantum phase
transition in an anisotropic central spin system. We find that this kind of
central spin systems can be mapped to the anisotropic Lipkin-Meshkov-Glick
model in the limit where the ratio of transition frequencies between the
central spin and the spin bath tends towards infinity. This property can induce
a one-axis twisting interaction and provides a new possibility for generating
spin squeezing. We separately consider generating spin-squeezed states via the
ground state and the dynamic evolution of the central spin model. The results
show that the spin squeezing parameter improves as the anisotropy parameter
decreases, and its value scales with system size as $N^{-2/3}$. Furthermore, we
obtain the critical exponent of the quantum Fisher information around the
critical point by numerical simulation, and find its value tends to $4/3$ as
the frequency ratio and the system size approach infinity. This work offers a
promising scheme for generating spin-squeezed state and paves the way for
potential advancements in quantum sensing.
