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 $Ngeqslant 3$. Finally, we also construct a class of strong nonlocality of entangled states in $dotimes dotimes cdots otimes d, dgeqslant 3$. Our results extend the phenomenon of strong nonlocality for entangled states.
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