Abstract: A penalty upwind finite element method is adopted to deal with the thermohaline double-diffusive system.The method has good stability and second-order accuracy. Natural convection with lateral heating in a square rectangular enclosure can be examined by this way, and it's solutions approximate to the results obtained with velocity-pressure Method. Afterwards, the method is employed for a two-dimensional, laminar, with lateral heating, steady double-diffusive convection partitioned by an adiabatic baffle. Main computation is for Ra=10⁶ and thermal buoyancy ratio N= 1,3,5,7. Distinct flow results depend on the magnitude of the thermal buoyancy ratio N and the baffle.