  In this work we study the dynamics of universe in $f(R)=\sqrt{R^2-R_{0}^2}$
modified gravity with Palatini formalism. We use data from recent observations
as Supernova Type Ia (SNIa) Gold sample and Supernova Legacy Survey (SNLS)
data, size of baryonic acoustic peak from Sloan Digital Sky Survey (SDSS), the
position of the acoustic peak from the CMB observations and large scale
structure formation (LSS) from the 2dFGRS survey to put constraint on the
parameters of the model. To check the consistency of this action, we compare
the age of old cosmological objects with the age of universe. In the combined
analysis with the all the observations, we find the parameters of model as
$R_0=6.192_{-0.177}^{+0.167}\times H_0^2$ and
$\Omega_m=0.278_{-0.278}^{+0.273}$.
