This paper study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of Cn. The final result we prove is: If f is a K-quasiconformal holomorphic mappings of the unit ball B of Cn such that det (f'(0)) = 1, then f(B)contains a schlicht ball of radius at least (CnK)1-n f01(1+t)n-1/(1-t)2 exp {-(n+1)t/1-t}dt where Cn > 1 is a constant depending on n only, and Cn→ 10 as n→∞.