In this paper, we firstly introduce a method to get a class of infinite-dimensional Lie algebra by Novikiov algebra. Then we recall the compatible Novikov alge- bra on Witt algebra, and we get a class of infinite-dimensional Lie algebra by using the mentioned method, is called Block type Lie algebra B(p; q). Finally, we study the representation theory for B(p; q). We prove that any quasifinite irreducible module of Block type Lie algebras B(p; q) is either a highest or lowest weight module, or else a uniformly bounded module. Furthermore, we also classify quasifinite irreducible highest weight B(p; q)-module.