  For any complex parameters a,b, the W(a,b) algebra is the Lie algebra with
basis {L_i,W_i|i\in Z}, and relations [L_i,L_j]=(j-i)L_{i+j},
[L_i,W_j]=(a+j+bi)W_{i+j},[W_i,W_j]=0. In this paper, indecomposable modules of
the intermediate series over W(a,b) are classified. It is also proved that an
irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight
module or a uniformly bounded module. Furthermore, if a\notin Q, an irreducible
weight W(a,b)-module is simply a Vir-module with trivial actions of W_k.
