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We concentrate on the cosmological properties in the Tsujikawa model (TM) ofviable $f(R)$ gravity with the dynamical background evolution and linearperturbation theory by using the CosmoMC package. We study the constraints ofthe cosmological variables along with the model parameter from the currentobservational data. In particular, we show that the matter density fluctuationis 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 theparameters of the deceleration and equation of state for dark energy in the TMand compare them with those in the $\Lambda$CDM model.

Cosmological evolutions in Tsujikawa model of $f(R)$ Gravity