  We investigate the interplay of the topological and Kondo effects in a
one-dimensional Kondo-Heisenberg model with nontrivial conduction band using
the density matrix renormalization group method. By analyzing the density
profile, the local hybridization, and the spin/charge gap, we find that the
Kondo effect can be destructed at the edges of the chain by the topological end
state below a finite critical Kondo coupling $J_{K}^{c}$. We construct a phase
diagram characterizing the transition of the end states.
