We give characterizations of a finite group $G$ acting symplectically on rational surface ($\mathbb{CP}^2$ blown up at two or more points). In particular, we obtain symplectic version the dichotomy $G$-conic bundles versus $G$-del Pezzo surfaces for corresponding $G$-rational surfaces, analogous to classical result in algebraic geometry. Besides (which is completely determined case $\mathbb{CP}...