In this paper, the authors characterize those φ, holomorphic self-maps of B, for which the composition operator C φ is bounded (or compact) on F(p,q,s) in some cases. Moreover, the following results are given. If 1<p<q + n + 1 and C φ satisfies some boundedness conditions, then C φ is compact on F(p,q,s) if and only if lim | z | → 1 − 1 − | z | 2 1 − | φ ( z ) | 2 = 0. If 1 ≤ p < ∞ and q + n + 1 < p < ∞ , then C φ is a compact operator on F(p,q,s) if and only if ‖ φ ‖ ∞ < 1 and φ l ∈ F ( p , q , s ) for all l ∈ { 1 , 2 , … , n } .