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In this paper, we study minimal surfaces in Randers space. We consider Randers metric $$F=\alpha +\beta $$ , on the 3-dimensional real vector space V, where $$\alpha $$ is the Euclidean metric, and $$\beta $$ is a 1-form with norm b satisfying $$0\le b<1$$ . We firstly solve the ordinary differential equation that characterizes the rotational minimal surfaces in ( V, F) and discuss the geometrical properties of the meridian curves. Then we obtain the ordinary differential equation that characterizing the minimal translation surface in ( V, F). Finally we prove that the only minimal surfaces in ( V, F) are plane. [ABSTRACT FROM AUTHOR]