  Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum
resource in quantum information processing such as quantum cryptography and
quantum communication. Many criteria have been proposed in the past few years
to detect steerability, both analytically and numerically, for bipartite
quantum systems. We propose effective criteria for tripartite steerability and
genuine tripartite steerability of three-qubit quantum states by establishing
connections between the tripartite steerability (resp. genuine tripartite
steerability) and the tripartite entanglement (resp. genuine tripartite
entanglement) of certain corresponding quantum states. From these connections,
tripartite steerability and genuine tripartite steerability can be detected
without using any steering inequalities. The ``complex cost'' of determining
tripartite steering and genuine tripartite steering can be reduced by detecting
the entanglement of the newly constructed states in the experiment. Detailed
examples are given to illustrate the power of our criteria in detecting the
(genuine) tripartite steerability of tripartite states.
