Abstract: Suppose \phi is an analytic map of the unit disk D into itself, X is a Banach space of analytic functions on D. Define the composition operator C_\phi: C_\phi(f)=f o \phi, for all f\in X. In this paper,we use K-carleson measure to discuss the bounded composition operators from B_\log^\alpha(B_\log,0^\alpha) to Q_k(p, q)(Q_k,0(p, q)) and the bounded and compact composition operators from B_\log^\alpha(B_\log,0^\alpha) to Q_k,0(p, q), where 0\alpha\infty.