Constructing 3-Lie algebras

3-Lie algebras are constructed by Lie algebras, derivations and linear functions, associative commutative algebras, whose involutions and derivations. Then the 3-Lie algebras are obtained from group algebras $F[G]$. An infinite dimensional simple 3-Lie algebra $(A,[,,{]}_{\omega ,{\delta }_0})$ and a non-simple 3-Lie algebra $(A,[,,{]}_{{\omega }_1,\delta })$ are constructed by Laurent polynomials $A=F[t,t^{-1}]$ and its involutions $\omega$ and ${\omega }_1$ and derivations $\delta$ and ${\delta }_0$. At last of the paper, we summarize the methods of constructing $n$-Lie algebras for $n\ge 3$ and provide a problem.