In this paper, we analyze the incompressible 3D chemotaxis system with gradient-dependent flux limitation and logistic source as follows: \(\begin{aligned}\,\, \left\{ \begin{aligned}&\partial _{t}\rho +u\cdot \nabla \rho =\Delta \rho -\nabla \cdot (\rho f(|\nabla c|^{2})\nabla c)+\gamma \rho -\mu \rho ^{3},\\&\partial _{t}c+u\cdot \nabla c=\Delta c -c\rho ,\\&\partial _{t}u+(u\cdot \nabla )u+\nabla P=\Delta u-\rho \nabla \phi ,\\&\nabla \cdot u=0. \end{aligned} \right. \end{aligned}\) Taking advantage of the structure of the axisymmetric without swirl, we obtain the unique global solution of the system with flux limitation \(f(\zeta )= K_{f}(1+\zeta )^{-\frac{k}{2}}\) for \(k>0\) .
