We propose a gravimeter based on a matter-wave resonant cavity loaded with a Bose–Einstein condensate and closed with a sequence of periodic Raman pulses. The gravimeter sensitivity increases quickly with the number of cycles experienced by the condensate inside the cavity. The matter wave is refocused thanks to a spherical wave-front of the Raman pulses. This provides a transverse confinement of the condensate which is discussed in terms of a stability analysis. We develop the analogy of this device with a resonator in momentum space for matter waves.