Abstract: A map φ on a Lie algebra g is called to be commuting if [φ（x）, x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P. 

Key words: commuting maps, finite-dimensional simple Lie algebras, standard parabolic subalgebras