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In this article, we prove that a $\mathbb{Q}$-homology plane $X$ with two algebraically independent $G_a$-actions is isomorphic to either the affine plane or a quotient of an affine hypersurface $xy=z^m-1$ in the affine $3$-space via a free $\mathbb{Z}/m\mathbb{Z}$-action, where $m$ is the order of a finite group $H_1(X;\mathbb{Z})$.