In this paper, we consider the following chemotaxis-Stokes system with nonlinear doubly degenerate diffusion \(\begin{aligned} {\left\{ \begin{array}{ll} \partial _{t}n+{{\textbf {u}}}\cdot \nabla n=\nabla \cdot \left( \arrowvert \nabla n^{m}\arrowvert ^{p-2}\nabla n^{m}\right) -\chi \nabla \cdot (n\nabla c) +n(r-\mu n^{\delta }),& (x,t)\in Q, \quad \\ \partial _{t}c+{{\textbf {u}}}\cdot \nabla c=\Delta c-nc,& (x,t)\in Q, \quad \\ \partial _{t}{{\textbf {u}}}=\Delta {{\textbf {u}}}+\nabla P+n\nabla \varPhi ,& (x,t)\in Q, \quad \\ \nabla \cdot {{\textbf {u}}}=0,& (x,t)\in Q, \quad \\ \end{array}\right. } \end{aligned}\) where \(Q=\Omega \times (0,\infty )\) , \(\Omega \subset {\mathbb {R}}^{3}\) is a smoothly bounded convex domain, \(m\geqslant 1\) , \(p\geqslant 2\) , \(\chi >0\) , \(r\in {\mathbb {R}}\) , \(\mu >0\) and \(\delta >1\) . Under the conditions of \(\delta >\frac{3}{2}\) , \(m\geqslant 1\) and \(p\geqslant 2\) satisfying \(p>\min \left\{ \frac{\left( 2\,m+4 \right) \delta +2-m}{\left( 2\delta -1\right) \left( m+1 \right) },\frac{2\left( \delta +m+1 \right) \delta }{\left( 2\delta +3 \right) \left( \delta -1 \right) } \right\} \) , it is shown that there exists a global bounded weak solution to the corresponding initial boundary problem.
