For two analytic self-maps φ and Ψ defined on the unit disk D,we characterize completely the boundedness and compactness of the difference Cφ-CΨ of the composition operators Cφ and CΨfrom Bloch space B into Besov space B∞v.Moreover,we also give a complete characterization of the compactness of the difference Cφ-CΨ on BMOA space.