We study the thermodynamic behavior of a hybrid
metric-Palatini gravity, which consists of adding to the
Einstein-Hilbert Lagrangian a f (R) term constructed within
the framework of the Palatini formalism. Using the respective
dynamically equivalent scalar tensor representation, we
investigate the verification of the first law and the generalized
second law (GSL) of thermodynamics on the dynamically
apparent horizon. We also examine the validity of the
GSL in a universe bounded by the cosmological event horizon
filled with the perfect fluid in this modified gravity theory.