We consider a parabolic-elliptic chemotaxis system with singular sensitivity and sublinear production: \(u_t=\Delta u-\chi \nabla \cdot \left( \frac{u}{v^\alpha } \nabla v\right) , 0=\Delta v-v+g(u)\) in a smooth bounded domain \(\Omega \subset {\mathbb {R}}^n(n \geqslant 2)\) with \(\chi >0, \alpha \in (0,1]\) , \(k_{1} u^{\beta _{1}}\leqslant g(u) \leqslant k_{2}u^{\beta _{2}}\) with \(\beta _{1},\beta _{2} \in (0,1)\) and \(k_{1}, k_{2}>0\) . It proved that the system possesses a globally bounded classical solution when \(\alpha \in (0,1)\) and \(\beta _{2}\in \left( 0, \frac{2}{n}\right) \) with \(\chi >0\) , or \(\alpha =1\) and \(\beta _{2} \in (0,1)\) with \(\chi \in (0, \min \{1,\frac{2}{n \beta _{2}}\})\) . This entails that sublinear productive effect is indeed benefit to ensure globally bounded classical solution to parabolic-elliptic chemotaxis with singular chemotactic mechanism.
