Abstract: In the paper, the hybrid laplace transform finite element method was used for solving solute transport problems of dynamic two-dimensional model of brine water in the first exploitation area, which can limitedly eliminate numerical diffusion and overdo phenomena from the solving convection dominated underwater solute transport problems, whose advantages were one step and local solving. And the method was used for convective-diffusion equation which have first derivative to test the numerical effectiveness and the capability to solve solute transport model.