A high-resolution spectrometer aimed at performing experiments of inelastic X-ray scattering by electronic excitations is described. The spectrometer has been installed at the D12A-XRD1 beamline of the National Synchrotron Light Laboratory (LNLS), in Campinas, Brazil. Synchrotron radiation is monochromated to about 6 keV and focused horizontally onto the sample by a sagittally focusing Si(111) double-crystal monochromator in non-dispersive setting. The spectrometer operates in Rowland circle geometry and is based on a focusing Si(333) analyser in near-backdiffraction geometry for energy analysis of inelastically scattered photons. The analyser works at a fixed Bragg angle, so energy transfers are obtained by varying the incident photon energy. A relative energy resolution of the whole spectrometer of approximately 1.5 x 10(-4) at 5.93 keV has been achieved. As an example of application, inelastic X-ray scattering by plasmon excitation in polycrystalline Be was measured. Test results demonstrate that inelastic X-ray scattering experiments with eV energy resolution and an acceptable counting rate are feasible at the LNLS when focused on plasmon and particle-hole excitations.