Abstract: The authors define the orders n cohomology groups and a binary function φ(·) of 3-Lie algebraA.Using the function,the authors define the Casimir operator of a representation.And obtain the main result that the orders two cohomology group H2 (A,V) of an non-degenerate 3-Lie algebra A is zero.

Key words: cohomology group, representation, nondegenerate, casimir operator