To study the boundedness of the Cauchy integrals over Lipschitz curves, new Hardy spaces H b p were introduced in [Y. Han, M.-Y. Lee and C.-C. Lin, Hardy spaces and the Tb theorem, J. Geom. Anal. 14 (2004) 291318], where b is a para-accretive function. In this paper, we define the Carleson measure spaces CMO b p that generalize BMO, and show that CMO b p is the dual space of H b p. As an application, we give a Carleson measure characterization of BMO b.