A method via extension was proposed to construct Lie algebra with Novikov structure over a field of characteristic zero.Using 2-cocycle and the representations of Lie algebras,the definition of extended Lie algebras was given by an Abelian Lie algebra and an arbitrary Lie algebra.A Lie algebra with Novikov structure is endowed with both affine structure and Novikov structure.With a proper product defined,the necessary and sufficient conditions for the extended Lie algebras endowed with affine structure was given.And the necessary and sufficient conditions for the extended Lie algebras endowed with Novikov structure was given.In practice the method is only suited to some special Lie algebras.An example was presented of the low-dimensional Lie algebra with the Novikov structure constructed by extension.