  In this letter we report our results in investigating edge effects of open
antiferromagnetic Heisenberg spin chains with spin magnitudes $S=1/2, 1,3/2,2$
using the density-matrix renormalization group (DMRG) method initiated by
White. For integer spin chains, we find that edge states with spin magnitude
$S_{edge}=S/2$ exist, in agreement with Valence-Bond-Solid model picture. For
half-integer spin chains, we find that no edge states exist for $S=1/2$ spin
chain, but edge state exists in $S=3/2$ spin chain with $S_{edge}=1/2$, in
agreement with previous conjecture by Ng. Strong finite size effects associated
with spin dimmerization in half-integer spin chains will also be discussed.
