This paper is devoted to a quasilinear preytaxis model with modified Leslie-Gower function and prey-induced acceleration \(\begin{aligned} {\left\{ \begin{array}{ll} u_{t}=\nabla (\phi (u)\nabla u)-\nabla (\psi (u){\textbf {w}})+u(a-\frac{u}{r_{1}+v}),& x\in \Omega ,t \in (0,\infty ),\\ v_{t}=d_v\Delta v+v(1-v)-\frac{uv}{r_{2}+v},& x\in \Omega ,t \in (0,\infty ),\\ {\textbf {w}}_t=d_w\Delta {\textbf {w}}+\gamma \nabla v,& x\in \Omega ,t\in (0,\infty ),\\ \end{array}\right. } \end{aligned}\) under the homogeneous Neumann and Dirichlet initial boundary in a convex smooth bounded domain \(\Omega \subset \mathbb {R}^2\) . The parameters satisfy \(d_{v},d_{w},a,\gamma > 0\) , \(r_{i}>0(i=1,2)\) , and the functions \(\phi (s)\ge d(s+1)^{\alpha }\) and \(0\le \psi (s)\le \chi s(s+1)^{\beta -1}\) , then we can prove the problem possesses a unique global classical solution. Moreover, when \(d_w\) is sufficiently large and certain conditions on \(r_i\) are met, we further prove that the steady-states of the preytaxis model are globally stable.
