In this paper, we consider the following chemotaxis-Stokes system with double chemical signals and quadratic damping effects \(\begin{aligned} \left\{ \begin{aligned}&n_{t}+u\cdot \nabla n=\Delta n-\chi \nabla \cdot (n \nabla c)-\xi \nabla \cdot (n \nabla v)+an-bn^2 & x\in \Omega ,t> 0,\\&c_{t}+u\cdot \bigtriangledown c=\bigtriangleup c-nc, & x\in \Omega ,t> 0,\\&v_{t}+u\cdot \bigtriangledown v=\bigtriangleup v-v+n, & x\in \Omega ,t> 0,\\&u_{t}+\bigtriangledown P =\bigtriangleup u+n\bigtriangledown \Phi & x\in \Omega ,t> 0,\\&\bigtriangledown \cdot u=0, & x\in \Omega ,t> 0 \end{aligned} \right. \end{aligned}\) in a smooth bounded domain \(\Omega \subset \mathbb {R}^3\) , with no-flux/no-flux/no-flux/Dirichlet boundary conditions, where \(\chi>0,\xi >0\) , \(a\in \mathbb {R}\) and \(b>0\) are given constants. We present that the chemotaxis-Stokes system admits a globally uniformly bounded classical solution for any suitably regular initial data in the case of \(b\ge \max \left\{ 33+\frac{45\xi ^2}{2}, \frac{45\chi ^2}{2}+39\left\| c_0\right\| ^2_{L^\infty (\Omega )}\right\} .\)
