Abstract: The potential equation is a typical second-order elliptic equation in the theoretical research of partial differential equations. In this paper，the Robin problem of the potential equation was studied deeply. We proved the uniqueness of its solution in C¹(Ω^-)?C²(Ω)by the divergence theorem. The conditions satisfied by the Green's function G（x，y）and the expression of its solution were derived by Green's function method.

Key words: potential equation, Robin problem, Green's function, elliptic equation