  Let $\BB$ be the Lie algebra of Block type with basis
$\{L_{\a,i}|\,\a,i\in\Z, i\geq0\}$ and relations
$[L_{\a,i},L_{\b,j}]=\left((\a-1)(j+1)-(\b-1)(i+1)\right)L_{\a+\b,i+j}$. In the
present paper, the derivation algebra and the automorphism group of $\BB$ are
explicitly described. In particular, it is shown that the outer derivation
space is 1-dimensional and the inner automorphism group of $\BB$ is trivial.
