A numerical investigation of unsteady, two-dimensional double diffusive convection flow through a lid-driven square enclosure is carried on. The left and bottom walls of the enclosure are either uniformly or non-uniformly heated and concentrated, while the right vertical wall is maintained at a constant cold temperature. The top wall is insulated and it moves to the right with a constant velocity. The numerical solution of the coupled nonlinear differential equations is based on the use of dual reciprocity boundary element method (DRBEM) in spatial discretization and an unconditionally stable backward implicit finite difference scheme for the time integration. Due to the coupling and the nonlinearity, an iterative process is employed between the equations. The boundary only nature of the DRBEM and the use of the fundamental solution of Laplace equation make the solution process computationally easier and less expensive compared to other domain discretization methods. The study focuses on the effects of uniform and non-uniform heating and concentration of the walls for various values of physical parameters on the double-diffusive convection in terms of streamlines, isotherms and isoconcentration lines.