| Let Bn be the unit ball in Cn and H(Bn) all holomorphic functions in Bn. Let0 <α<∞. f belongs toα-Bloch space Bα(Bn), if f∈H(Bn) andLet 0 < p,s <∞,?n?1 < q <∞and q +s > ?1. f belongs to F(p,q,s) if f∈H(Bn)andLet ? be the analytic self-mapping on Bn. Composition operator C? is de?ned as:The essential norm of linear operator T is de?ned as:Estimates of the essential norm of composition operator between Bloch-type spaces andfrom F(p,q,s) to Bloch-type space are obtained in this paper. At the same time, weget the su?cient and necessary conditions for the composition operators to be compactor bounded.
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