  The Palatini $f(R)$ gravity, is able to probably explain the late time cosmic
acceleration without the need for dark energy, is studied. In this paper, we
investigate a number of $f(R)$ gravity theories in Palatini formalism by means
of statefinder diagnosis. We consider two types of $f(R)$ theories: (i)
$f(R)=R+\alpha R^{m}-\beta R^{-n}$ and (ii) $f(R)=R+\alpha ln R+\beta$. We find
that the evolutionary trajectories in the $s-r$ and $q-r$ planes for various
types of the Palatini $f(R)$ theories reveal different evolutionary properties
of the universe. Additionally, we use the observational $H(z)$ data to
constrain models of $f(R)$ gravity.
