The authors study the central extensions of some generalized Virasoro-like algebras \(L(\alpha, \beta)\), then construct a class of Harish-Chandra modules \(V(a,b)\) over the generalized Virasoro algebra \(L(\alpha, \beta)\), and find necessary and sufficient conditions for \(V(a,b) \simeq V(a',b')\) and the reducibility of \(V(a,b)\).