Let \({\mathfrak g}\) be a Virasoro algebra over a quadratically closed field of characteristic 0. The authors determine the structures of \(H^ 1 ({\mathfrak g}, M_{(4,1)})\), \(H^ 2 ({\mathfrak g}, M_{(4,2)})\) and \(H^ 2 ({\mathfrak g}, M_ L)\), where \(M_{(4,1)}\), \(M_{(4,2)}\) are two classes of a basic Harish-Chandra module, \(M_ L\) is the space of Laurent polynomials in one variable without constant term.