  Recently, Halder \emph{et al.} [S. Halder \emph{et al.}, Phys. Rev. Lett.
\textbf{122}, 040403 (2019)] present two sets of strong nonlocality of
orthogonal product states based on the local irreducibility. However, for a set
of locally indistinguishable orthogonal entangled states, the remaining
question is whether the states can reveal strong quantum nonlocality. Here we
present a general definition of strong quantum nonlocality based on the local
indistinguishability. Then, in $2 \otimes 2 \otimes 2$ quantum system, we show
that a set of orthogonal entangled states is locally reducible but locally
indistinguishable in all bipartitions, which means the states have strong
nonlocality. Furthermore, we generalize the result in N-qubit quantum system,
where $N\geqslant 3$. Finally, we also construct a class of strong nonlocality
of entangled states in $d\otimes d\otimes \cdots \otimes d, d\geqslant 3$. Our
results extend the phenomenon of strong nonlocality for entangled states.
