Within the approximation of dominant charging collisions the explicit microscopic calculations of the Fokker-Planck kinetic coefficients for highlycharged grains moving in plasma are performed. It is shown that due to ion absorption by grain the friction coefficient can be negative and thus the appropriate threshold value of the grain charge is found. The stationary solutions of the Fokker-Planck equation with the velocity dependent kinetic coefficient are obtained and a considerable deviation of such solutions from the Maxwellian distribution is established. Lw, 52.20.Hv, 52.25.Fi Description of the Brownian motion in the systems with particle or energy fluxes still remains one of the key problems in the statistical physics of the open systems [1]. Starting from the classical Lord Rayleigh work [2] many studies of the nonequilibrium motion of Brownian particles with additional (inner or external) energy supply have been performed. In particular, such studies are of great importance for physical-chemical [3,4] and biological [5] systems in which non-equilibrium Brownian particle motion is referred to as the motion of active Brownian particles. Recently the dynamical and energetic aspects of motion for the active Brownian particles have been described based on the Langevin equation and the appropriate FokkerPlanck equation [6,7]. The possibility of negative friction (negative values of friction coefficient) of the Brownian particles was regarded as a result of energy pumping. *