In this talk I will introduce the classification result on the graded left-symmetric algebraic structures on Witt and Virasoro algebras. The classification is based on that any compatible left-symmetric algebraic structure on the Witt Lie algebra W is simple and is an indecomposable W-module with one-dimensional weight-spaces, i.e., an indecomposable intermediate series module. This is a joint work with Chengming Bai and Xiaoli Kong.