In this paper, we deal with the following system with nonlinear signal consumption under homogeneous Neumann boundary conditions in a smooth bounded domain $\Omega \in {\mathbb{R}^n} \left( {n \ge 2} \right)$. It shown that whenever $r > 0,\mu > 0,\alpha > 2, \beta > 0 \text{ and } \frac{\alpha }{\beta } > \frac{{n + 2}}{2}$,then the original system will produce a global classical solution and the solution converges to equilibrium \ \noindent{\bf Keywords}: Global existence; Boundedness; Signal-dependent motilities; Large time behavior. \ \noindent{\bf AMS(2020) Subject Classification}: 35A01, 35B65, 35K65, 35Q92, 92C17.