We say that a graded ring ( $ * $ -ring) $ R $ is a graded quasi-Baer ring (graded quasi-Baer $ * $ -ring)if, for each graded ideal $ I $ of $ R $ , the right annihilator of $ I $ is generated by a homogeneous idempotent (projection).We prove that a Leavitt pathalgebra is quasi-Baer (quasi-Baer $ * $ ) if and only if it is graded quasi-Baer (graded quasi-Baer $ * $ ).We show that a Leavitt path algebra is quasi-Baer (quasi-Baer $ * $ ) if its zero component is quasi-Baer (quasi-Baer $ * $ ).However, we give some example that showing that the converse implication fails.Finally, we characterize the Leavitt path algebras that are quasi-Baer $ * $ -ringsin terms of the properties of the underlying graph.
