  To investigate whether $f(R)$ gravity can relieve current $H_0$ and
$\sigma_8$ tensions, we constrain the Hu-Sawicki $f(R)$ gravity with
Planck-2018 cosmic microwave background and redshift space distortions
observations. We find that this model fails to relieve both $H_0$ and
$\sigma_8$ tensions, and that its two typical parameters $\log_{10}f_{R0}$ and
$n$ are insensitive to other cosmological parameters. Combining the cosmic
microwave background, baryon acoustic oscillations, Type Ia supernovae, cosmic
chronometers with redshift space distortions observations, we give our best
constraint $\log_{10}f_{R0}<-6.75$ at the $2\sigma$ confidence level.
