  Let B be the Lie algebra with basis {L_{i,j},C|i,j\in Z} and relations
[L_{i,j},L_{k,l}]=((j+1)k-i(l+1))L_{i+k,j+l}+i\delta_{i,-k}\delta_{j+l,-2}C,
[C,L_{i,j}]=0. It is proved that an irreducible highest weight B-module is
quasifinite if and only if it is a proper quotient of a Verma module. For an
additive subgroup G of the base field F, there corresponds to a Lie algebra
B(G) of Block type. Given a totalorder \succ on G and a weight \Lambda, a Verma
B(G)-module M(\Lambda,\succ) is defined. The irreducibility of M(\Lambda,\succ)
is completely determined.
