We investigate stationary, spherically symmetric accretion of the relativistic Vlasov gas on Reissner-Nordström black holes. The model is based on a recent analysis done by Rioseco and Sarbach for the Schwarzschild spacetime. Both models share many common features: The gas characterized by the Maxwell-Jüttner distribution at infinity is no longer in thermal equilibrium in the vicinity of the black hole. The radial pressure at the black hole horizon can even be an order of magnitude smaller than the tangential pressure. Quantitative characteristics of the Reissner-Nordström model depend on the charge parameter. For black holes with fixed asymptotic mass, the mass accretion rate decreases with the increasing black hole charge. The ratio of the tangential pressure to the radial pressure at the horizon also decreases with the increasing charge. On the other hand, the particle density at the horizon (normalized by its asymptotic value) grows with the black hole charge parameter.