  A homothetical surface arises as a graph of a function $z = \varphi_1(v_1)
\varphi_2(v_2)$. In this paper, we study the homothetical surfaces in three
dimensional psuedo-Galilean space$\left(\mathbb{G}_3^1\right)$ satisfying the
conditions $\Delta^{II}\textbf{x}_i=\lambda_i\textbf{x}_i,$ where $\Delta^{II}$
is the Laplacian with respect to second fundamental form. In particular, we
show the non-existence of any such type of surface in $\mathbb{G}_3^1.$
