The dynamics of inviscid multi-component relativistic fluids may be modeled by the relativistic Euler equations, augmented by one (or more) additional species equation(s). We use the high-resolution staggered central schemes to solve these equations. The equilibrium states for each component are coupled in space and time to have a common temperature and velocity. The current schemes can handle strong shocks and the oscillations near the interfaces are negligible, which usually happens in the multi-component flows. The schemes also guarantee the exact mass conservation for each component, the exact conservation of total momentum, and energy in the whole particle system. The central schemes are robust, reliable, compact and easy to implement. Several one- and two-dimensional numerical test cases are included in this paper, which validate the application of these schemes to relativistic multi-component flows.