  In this paper, we study the time periodic problem to a three-dimensional
chemotaxis-Stokes model with porous medium diffusion $\Delta n^m$ and
inhomogeneous mixed boundary conditions. By using a double-level approximation
method and some iterative techniques, we obtain the existence and time-space
uniform boundedness of weak time periodic solutions for any $m>1$. Moreover, we
improve the regularity for $m\le\frac{4}{3}$ and show that the obtained
periodic solutions are in fact strong periodic solutions.
