The general field of the invention is that of matter-wave gravimeters. The gravimeter according to the invention comprises at least: means for generating, for capturing and for cooling a cloud of ultra-cold atoms; means of transferring the atoms into a superposition, with equal weights, of a first internal electronic state called state |1>) and of a second internal electronic state called state |2> comprising the application of at least a first microwave field and of a radiofrequency field; means for separating the atoms into two wave packets for a given period of time under the effect of at least a second microwave field, the said separation leading to a phase-shift associated with the local gravitational field; calibration means allowing a “magic” magnetostatic field to be determined for which the difference in energy between the first internal electronic state and the second internal electronic state is independent, to a first order, of the fluctuations of the magnetostatic field.