  Block type Lie algebras have been studied by many authors in the latest
twenty years. In this paper, we will study a class of more general Block type
Lie algebra $\mathcal{B}(p,q)$, which is a class of infinite-dimensional Lie
algebra by using the generalized Balinskii-Novikov's construction method to
Witt type Novikov algebra. We study the representation theory for
$\mathcal{B}(p,q)$. We classify quasifinite irreducible highest weight
$\mathcal{B}(p,q)$-module. We also prove that any quasifinite irreducible
module of Block type Lie algebras $\mathcal{B}(p,q)$ is either a highest or
lowest weight module, or else a uniformly bounded module. This paper can be
considered as a generalization of the related literatures.
