  We concentrate on the cosmological properties in the Tsujikawa model (TM) of
viable $f(R)$ gravity with the dynamical background evolution and linear
perturbation theory by using the CosmoMC package. We study the constraints of
the cosmological variables along with the model parameter from the current
observational data. In particular, we show that the matter density fluctuation
is suppressed and the constraint of the neutrino mass sum is relaxed in the TM,
which are similar to other viable $f(R)$ models. In addition, we discuss the
parameters of the deceleration and equation of state for dark energy in the TM
and compare them with those in the $\Lambda$CDM model.
