The authors consider the Keller-Segel-Navier-Stokes system in a bounded domain \[ \begin{aligned} \partial_t u+u\cdot \nabla u+\nabla\pi-\Delta u+n\nabla\phi=0,\text{ in } \Omega\times(0,\infty),\\ \operatorname{div} u=0,\text{ in }\Omega\times(0,\infty),\\ \partial_t n+u\cdot \nabla n-\Delta n=-\nabla\cdot(n\nabla p)-\nabla\cdot(n\nabla q),\text{ in }\Omega\times(0,\infty),\\ \partial_tp+u\cdot\nabla p-\Delta p=-np,\text{ in } \Omega\times(0,\infty),\\ \partial_tq+u\cdot\nabla q-\Delta q+q=n,\text{ in } \Omega\times(0,\infty),\\ u=0,\quad\frac{\partial n}{\partial\nu}=\frac{\partial p}{\partial\nu}=\frac{\partial q}{\partial\nu}=0,\text{ on } \partial\Omega\times(0,\infty),\\ (u,n,p,q)(\cdot,0)=(u_0,n_0,p_0,q_0)(\cdot),\text{ in }\Omega\subset\mathbb{R}^3, \end{aligned} \] where \(u\) denotes the velocity of the fluid and \(\pi\) is the pressure, \(n\), \(p\) and \(q\) denote the density of amoebae, oxygen and chemical attractant, respectively. The function \(\phi\) is a potential function. \(\Omega\) is a bounded domain in \(\mathbb{R}^3\) with smooth boundary \(\partial\Omega\), \(\nu\) is the unit outward normal vector to \(\partial\Omega\). The authors prove some blow-up criteria of the local strong solutions.