Double diffusive flow in a cavity has attracted lots of attention due to its importance in many engineering fields such as ocean circulation, crystal growth, pollution transportation in air, metal manufacturing process and so on. When heat and mass transfer occur simultaneously in the double diffusive flow, the fluid flow is not only driven by the temperature gradient but also by the concentration gradient as well. In some cases, the Dufour and Soret effects will play a significant role in the double diffusive flow process. The energy flux created by the concentration gradient is called Dufour effect and the temperature gradient can cause the mass flux which is Soret effect. When taking the Soret and Dufour effects into account, the temperature and concentration equations become coupled with each other. However, the coupling diffusivities matrix can be diagonalized. The coupled system can then be transformed to two uncoupled diffusion-advection equations of two independent species. The temperature and concentration can be obtained by the inverse transformation of these two independent species. As a numerical method developed in the past two decades, lattice Boltzmann method (LBM) is powerful in simulating complex heat transfer and fluid mechanics problems. In the current study, a lattice Boltzmann model was developed and implemented for the double-diffusive convection with Soret and Dufour effects. Three distribution functions were used to compute the fluid velocity, specie 1, and specie 2, respectively. Specifically, a rectangular enclosure with horizontal temperature and concentration gradients was investigated. On the other hand, the graphics processing units (GPU) computing becomes popular since the advent of the NVIDIA's CUDA platform, which includes both hardware components and software programming environment. The developed LBM code was adapted on the CUDA platform to accelerate the computation for parametric studies. The GPU is responsible for the parallel tasks while CPU tackles the sequential steps in the computation. To verify the improvement on computation ability by using GPU, the ratio of the computational time between CPU code and CUDA code is presented by simulating the classical natural convection process in a cavity. The computational speed can be accelerated by more than 20 times when large number of nodes is used. The fluid flow, temperature field and concentration field are presented for different Rayleigh numbers, buoyancy ratios, Prandtl numbers, Lewis numbers, aspect ratios, as well as Soret and Dufour coefficients. In addition, the results of Nusselt and Sherwood numbers are shown for different parametric conditions. As a result, lattice Boltzmann method was demonstrated as a good option to study the complex double-diffusive convection with Soret and Dufour effects in a vertical cavity.