  In the context of modified $f(R)$ gravity, we attempt to study the
thermodynamic properties of the evolving Lorentzian wormholes at the apparent
horizon. It is shown that the wormhole can be derived from a particular $f(R)$
model in the radiation background. Moreover, it has been shown that the field
equations can be cast to a similar form $dE = TdS + WdV + Td\bar{S}$ at the
apparent horizon for the evolving Lorentzian wormhole. Compared to the case of
Einstein's general relativity, an additional term $Td\bar{S}$ appears here.
