In this paper, we investigate the global existence of classical solution to the following parabolic–parabolic–parabolic chemotaxis system with singular sensitivity 0.1 \(\begin{aligned} {\left\{ \begin{array}{ll} u_t=\Delta u-\chi _1\nabla \cdot (\frac{u}{w}\nabla w)+f_1(u,v), & t>0,~x\in \Omega ,\\ v_t=\Delta v-\chi _2\nabla \cdot (\frac{v}{w}\nabla w)+f_2(u,v), & t>0,~x\in \Omega ,\\ w_t=\Delta w-w+u+v, & t>0,~x\in \Omega ,\\ \frac{\partial u}{\partial \nu }=\frac{\partial v}{\partial \nu }=\frac{\partial w}{\partial \nu }=0, & t>0,~x\in \partial \Omega ,\\ u(0,x)=u_0(x),~~v(0,x)=v_0(x),~~w(0,x)=w_0(x), & x\in \Omega , \end{array}\right. } \end{aligned}\) where \(\Omega \subset {\mathbb {R}}^N(N\ge 1)\) is a bounded smooth domain, and the parameters \(\chi _1\) and \(\chi _2\) are positive constants, \(f_1,f_2\in C^1[0,\infty )\) satisfy \(f_1(u,v)+f_2(u,v)\le a(u+v)-b(u+v)^\gamma \) with \(a\ge 0\) and \(b,\gamma >0.\) We prove that the problem (0.1) possesses a global and classical solution as long as \(\gamma >2.\)
