  We investigate the low-temperature properties of the spin-1 antiferromagnetic
Heisenberg chain with bond-alternation by the quantum Monte Carlo method (loop
algorithm). The strength of bond-alternation at the gapless point is estimated
as $\delta_{c}=0.2595\pm0.0005$. We confirm numerically that the
low-temperature properties at the gapless point are consistent with field
theoretical predictions. The numerical results are compared with those of the
spin-1/2 antiferromagnetic Heisenberg chain and recent experimental results for
[\{Ni(333-tet)($\mu$-N$_3$)\}$_n$](ClO$_4$)$_n$ (333-tet=tetraamine
$N,N^{\prime}$-bis(3-aminopropyl)-1,3-propanediamine).
