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In this paper we completely solve a simple quartic family of Thue equationsover $\mathbb{C}(T)$. Specifically, we apply the ABC-Theorem to find allsolutions $(x,y) \in \mathbb{C}[T] \times \mathbb{C}[T]$ to the set of Thueequations $F_{\lambda}(X,Y) = \xi$, where $\xi \in \mathbb{C}^{\times}$ and\begin{equation*} F_{\lambda}(X,Y):=X^4 -\lambda X^3Y -6 X^2Y^2 + \lambda XY^3+Y^4, \quad \quad \lambda \in \mathbb{C}[T]/\{\mathbb{C}\} \end{equation*}denotes a family of quartic simple forms.

Thue equations over $\mathbb{C}(T)$: The Complete Solution of a Simple quartic family