  In this paper, we study the boundedness and the compactness of the little
Hankel operators $h_b$ with operator-valued symbols $b$ between different
weighted vector-valued Bergman spaces on the open unit ball $\mathbb{B}_n$ in
$\mathbb{C}^n.$ More precisely, given two complex Banach spaces $X,Y,$ and $0 <
p,q \leq 1,$ we characterize those operator-valued symbols $b:
\mathbb{B}_{n}\rightarrow \mathcal{L}(\overline{X},Y)$ for which the little
Hankel operator $h_{b}: A^p_{\alpha}(\mathbb{B}_{n},X) \longrightarrow
A^q_{\alpha}(\mathbb{B}_{n},Y),$ is a bounded operator. Also, given two
reflexive complex Banach spaces $X,Y$ and $1 < p \leq q < \infty,$ we
characterize those operator-valued symbols $b: \mathbb{B}_{n}\rightarrow
\mathcal{L}(\overline{X},Y)$ for which the little Hankel operator $h_{b}:
A^p_{\alpha}(\mathbb{B}_{n},X) \longrightarrow A^q_{\alpha}(\mathbb{B}_{n},Y),$
is a compact operator.
