  {\bf{CONTEXT}}: In this work we propose a modified gravity action
$f(R)=(R^n-R^n_{0})^{1/n}$ with two free parameters of $n$ and $R_{0}$ and
derive the dynamics of a universe for this action in the Palatini formalism.
{\bf {AIM}}: We do a cosmological comparison of this model with observed data
to find the best parameters of a model in a flat universe. {\bf{METHOD}}: To
constrain the free parameters of model we use SNIa type Ia data in two sets of
gold and union samples, CMB-shift parameter, baryon acoustic oscillation, gas
mass fraction in cluster of galaxies, and large-scale structure data. {\bf
{RESULT}}: The best fit from the observational data results in the parameters
of model in the range of $n=0.98^{+0.08}_{-0.08}$ and $\Omega_M =
0.25_{+0.1}^{-0.1}$ with one sigma level of confidence where a standard
$\Lambda$CDM universe resides in this range of solution.
  PACS numbers: 04.50.+h, 95.36.+x, 98.80.-k
