  We investigate the viable exponential $f(R)$ gravity in the metric formalism
with $f(R)=-\beta R_s (1-e^{-R/R_s})$. The latest sample of the Hubble
parameter measurements with 23 data points is used to place bounds on this
$f(R)$ model. A joint analysis is also performed with the luminosity distances
of Type Ia supernovae and baryon acoustic oscillations in the clustering of
galaxies, and the shift parameters from the cosmic microwave background
measurements, which leads to $0.240<\Omega_m^0<0.296$ and $\beta>1.47$ at
1$\sigma$ confidence level. The evolutions of the deceleration parameter $q(z)$
and the effective equations of state $\omega_{de}^{eff}(z)$ and
$\omega_{tot}^{eff}(z)$ are displayed. By taking the best-fit parameters as
prior values, we work out the transition redshift (deceleration/acceleration)
$z_T$ to be about 0.77. It turns out that the recent observations are still
unable to distinguish the background dynamics in the $\Lambda$CDM and
exponential $f(R)$ models.
