The radial basis function (RBF) collocation methods are meshless with spectrally accurate; its approximation is an extremely powerful tool for solving various types of partial differential equations (PDEs). In this paper, the Gaussian RBF (G-RBF) collocation method is applied to solving unsteady groundwater flow governed by nonlinear elliptic PDEs. During the whole solution process, no iterations are required for a kind of nonlinear PDEs. Numerical results are compared with the well-known Kansa's method, also namely as Multiquadrics radial basis function (MQ-RBF). The results obtained show good performance of the G-RBF as solution to unsteady groundwater flow problems.