  We investigate the generalized second law (GSL) of thermodynamics in the
framework of $f(R)$-gravity. We consider a FRW universe filled only with
ordinary matter enclosed by the dynamical apparent horizon with the Hawking
temperature. For a viable modified gravity model as $f(R)=R-\alpha/R+\beta
R^{2}$, we examine the validity of the GSL during the early inflation and late
acceleration eras. Our results show that for the selected $f(R)$-gravity model
minimally coupled with matter, the GSL in the early inflation epoch is
satisfied only for the special range of the equation of state parameter of the
matter. But in the late acceleration regime, the GSL is always respected.
