A nonlinear mechanism of kinetic Alfven waves (KAW) generation on dust plasma with small plasma parameter β is proposed. A nonlinear dispersion equation describing three-wave interaction is obtained on the basis of three-fluid magnetohydrodynamics. In the dynamics of dusty Alfven waves, the kinetic effects (finite Larmor radius of dust grains) are taken into account. The instability growth rates and the time of instability development, which depend on dusty plasma parameters, are found. Our theoretical investigation show that the Alfven mode in the dusty plasma can be an effective source of the dusty kinetic Alfven waves. This nonlinear process can take place in the Earth's magnetosphere and ionosphere, in interstellar clouds, in tails of comets, in giant planetary rings and in other space objects.