In this paper, the chemotaxis-Stokes system with slow $p$-Laplacian diffusion and logistic source as follows

$$\{\begin{array}{rlr}& n_t+u\cdot \mathrm{\nabla }n=\mathrm{\nabla }\cdot (|\mathrm{\nabla }n{|}^{p-2}\mathrm{\nabla }n)-\mathrm{\nabla }\cdot (n\mathrm{\nabla }c)+\mu n(1-n),& x\in \mathrm{\Omega },t>0,\\ & c_t+u\cdot \mathrm{\nabla }c=\mathrm{\Delta }c-cn,& x\in \mathrm{\Omega },t>0,\\ & u_t+\mathrm{\nabla }P=\mathrm{\Delta }u+n\mathrm{\nabla }\mathrm{\Phi },& x\in \mathrm{\Omega },t>0,\\ & \mathrm{\nabla }\cdot u=0,& x\in \mathrm{\Omega },t>0\end{array}$$

was considered in a bounded domain $\mathrm{\Omega }\subset {\mathbb{R}}^3$ with smooth boundary under homogeneous Neumann-Neumann-Dirichlet boundary conditions. Subject to the effect of logistic source, we proved the system exists a global bounded weak solution for any $p>2$.