The fine-structure constant α is a crucial parameter of the quantum electrodynamics theory especially for evaluating the magnetic moment of electron or muon predicted by the standard model. By using a matter-wave interferometer to measure the recoil velocity, we obtained recently a new value of the fine-structure constant with an accuracy of 81 parts per trillion. Using this value of the fine-structure constant, we obtained a prediction of the anomalous magnetic moment of the electron with a relative uncertainty below 0.1 ppt. This is the most accurate prediction of the standard model. This result is an important step in the way of testing, in the electron sector, the discrepancy observed in the magnetic moment anomaly of the muon.