Lattice Boltzmann method of two-and three-dimensional thermosolutal convection is investigated in this paper. Lattice Boltzmann method with multiple components was applied to simulate two-dimensional thermosolutal convection flow on a square cavity. The numerical results agree well with those of high order finite difference method. It shows that the numerical scheme is efficient. Therefore the lattice Boltzmann method is extended to investigate three-dimensional thermosolutal convection flow in cubic cavity. The comparison between the proposed lattice Boltzmann method and a finite difference method shows a satisfactory agreement. The limitation of the lattice Boltzmann model in the double-diffusive convection is discussed.