  In this paper, we study the structure of 3-Lie algebras with involutive
derivations. We prove that if $A$ is an $m$-dimensional 3-Lie algebra with an
involutive derivation $D$, then there exists a compatible 3-pre-Lie algebra
$(A, \{ , , , \}_D)$ such that $A$ is the sub-adjacent 3-Lie algebra, and there
is a local cocycle $3$-Lie bialgebraic structure on the $2m$-dimensional
semi-direct product 3-Lie algebra $A\ltimes_{ad^*} A^*$, which is associated to
the adjoint representation $(A, ad)$. By means of involutive derivations, the
skew-symmetric solution of the 3-Lie classical Yang-Baxter equation in the
3-Lie algebra $A\ltimes_{ad^*}A^*$, a class of 3-pre-Lie algebras, and eight
and ten dimensional local cocycle 3-Lie bialgebras are constructed.
