  We study the $S=1$ quantum spin chain with bond alternation ${\cal H}=\sum _i
(1-(-1)^i\delta)\vect{S}_i\cdot \vect{S}_{i+1}$ by the density matrix
renormalization group method recently proposed by Steven R. White
(\PRL{69}{3844}{1993}). We find a massless point at $\delta _c =0.25 \pm 0.01$.
We also find the edge states in the region $\delta <\delta_c$ under the open
boundary condition, which disappear in the region $\delta >\delta _{c}$. At the
massless point, the spin wave velocity $v_s$ is $3.66 \pm 0.10$ and the central
charge $c$ is $1.0\pm 0.15$. Our results indicate that a continuous phase
transition occurs at the massless point $\delta =\delta_c $ accompanying
breaking of the hidden $Z_2\times Z_2$ symmetry.
