  An accurate prediction of the geo-neutrino signal from the crust serves as a
necessary prerequisite in the determination of the geo-neutrino flux from the
mantle. In this work we report the non-negligible effect associated to the
exact three-flavor antineutrino survival probability in the calculation of the
crustal geo-neutrino signal, which was usually approximated as a constant
average in previous studies. A geo-neutrino signal underestimation of about 1-2
TNU is observed as a result of the oscillatory behaviour within the local
crustal region extending for about 300 km from the experimental site. We also
estimated that the Mikheyev-Smirnov-Wolfenstein matter oscillation is
responsible for a $0.1\%$-$0.3\%$ increase of the local crustal signal,
depending on the detector location. This work reminds that the exact
oscillation possibility in matter should be considered for future prediction of
the local crustal geo-neutrino signal.
