Let $D$ be a bounded balanced domain with $C^{1}$ plurisubharmonic defining functions in ${\mathbf C}^{n}$. First, we give a necessary and sufficient condition that a locally biholomorphic mapping from $D$ to ${\mathbf C}^{n}$ is starlike. Next, we give a growth theorem for normalized starlike mappings on $D$. We also give a quasiconformal extension of some strongly starlike mapping on $D$.