In this paper, we deal with the following Neumann-initial boundary value problem for a quasilinear chemotaxis model describing tumor angiogenesis: \( {\left\{ \begin{array}{ll} u_t = \nabla \cdot (D(u)\nabla u) - \chi \nabla \cdot (u\nabla v) + \xi _1\nabla \cdot (u^m\nabla w) , & x\in \Omega ,\ t> 0, \\ v_t = \Delta v + \xi _2\nabla \cdot (v\nabla w) - v + u, & x\in \Omega ,\ t> 0, \\ 0 = \Delta w - w + u, & x\in \Omega ,\ t> 0, \\ {\frac{\partial u}{\partial \nu } = \frac{\partial v}{\partial \nu } = \frac{\partial w}{\partial \nu } = 0, }& {x\in \partial \Omega ,\ t > 0, }\\ {u(x,0) = u_0(x),\ v(x,0) = v_0(x),} & { x\in \Omega ,} \end{array}\right. } \) in a bounded smooth domain \(\Omega \subset \mathbb {R}^n (n\le 3)\) , where the parameter \(\chi , \xi _1,\xi _2 > 0\) , \(D(u)\) is supposed to satisfy the following property \( D(u) \ge (u + 1)^\alpha \text { with } \alpha > 0. \) Assume that \(\xi _1\ge \lambda _1^*\chi ^2\) , where the parameter \(\lambda _1^* = \lambda _1^*(u_0, v_0, \Omega ) > 0\) ; then the system admits a global classical solution (u, v, w) via subtle energy estimates. Moreover, it is asserted that the corresponding solution exponentially converges to the constant stationary solution \((\bar{u}_0, \bar{u}_0, \bar{u}_0)\) provided the initial data \(u_0\) is sufficiently small, where \(\bar{u}_0 = \frac{\int _\Omega u_0}{|\Omega |}\) .
