  As one of the most intriguing features of quantum mechanics,
Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum
networks. Greenberger-Horne-Zeilinger (GHZ) state plays important role in
quantum communication network. By reconstructing the covariance matrix of a
continuous variable tripartite GHZ state, we fully quantify the amount of
bipartite steering under Gaussian measurements. We demonstrate that the
(1+1)-mode steerability is not exist in the tripartite GHZ state, only the
collectively steerability exist between the (1+2)-mode and (2+1)-mode
partitions. These properties confirm that the tripartite GHZ state is a perfect
resource for quantum secret sharing protocol. We also demonstrate one-way EPR
steering of the GHZ state under Gaussian measurements, and experimentally
verify the introduced monogamy relations for Gaussian steerability. Our
experiment provides reference for using EPR steering in Gaussian GHZ states as
a valuable resource for multiparty quantum information tasks.
