This paper presents an analytical solution for two-dimensional non-axisymmetric solute transport in a radially convergent flow field. We applied a Laplace-transformed power series (LTPS) technique to solve the two-dimensional advection-dispersion equation in cylindrical coordinates. The solution is compared with a numerical solution to evaluate its robustness and accuracy. The applicable Péclet number range of the developed power series solution is also examined. Results show that the LTPS technique can effectively and accurately handle the two-dimensional radial advection-dispersion equation for a Péclet number up to 60. The two-dimensional power series solution is appropriate for hydrogeologic circumstances where temporally and spatially continuous solutions are demanded.