  In this paper we revisit the topic of Hawking radiation as tunneling. We show
that the imaginary part of the action of the tunneling particle should be
reconstructed in a covariant way, as a line integral along the classical
forbidden trajectory of tunneling particles. As the quantum tunneling
phenomenon, the probability of tunneling is related to the imaginary part of
the action for the classical forbidden trajectory. We do the calculations for
massless and massive particles, in Schwarzschild coordinate and Painlev\'e
coordinate. The construction of particle action is invariant under coordinate
transformations, so this method of calculation black hole tunneling does not
have the so called "factor 2 problem". As an application, we find that the
temperature of Hawking temperature of apparent horizon in a FRW universe is
$T=\frac{\kappa}{2\pi}$. Based on this result, we briefly discuss the unified
first law of apparent horizon in FRW universe.
