Context. Coronal mass ejections (CMEs) are large eruptions of plasma and magnetic field from the Sun’s corona. Understanding the evolution of the CME is important to evaluate its impact on space weather. Using numerical simulation, we are able to reproduce the occurrence and evolution process of the CME. Aims. The aim of this paper is to provide a new data-driven method to mimic the coronal mass ejections. By using this method, we can investigate the phsical mechanisms of the flux rope formation and the cause of the CME eruption near the real background. Methods. Starting from a potential magnetic field extrapolation, we have solved a full set of magnetohydrodynamic (MHD) equations by using the conservation element and solution element (CESE) numerical method. The bottom boundary is driven by the vector magnetograms obtained from SDO/HMI and vector velocity maps derived from DAVE4VM method. Results. We present a three-dimensional numerical MHD data-driven model for the simulation of the CME that occurred on 2015 June 22 in the active region NOAA 12371. The numerical results show two elbow-shaped loops formed above the polarity inversion line (PIL), which is similar to the tether-cutting picture previously proposed. The temporal evolutions of magnetic flux show that the sunspots underwent cancellation and flux emergence. The signature of velocity field derived from the tracked magnetograms indicates the persistent shear and converging motions along the PIL. The simulation shows that two elbow-shaped loops were reconnected and formed an inverse S-shaped sigmoid, suggesting the occurrence of the tether-cutting reconnection, which was supported by observations of the Atmospheric Imaging Assembly (AIA) telescope. Analysis of the decline rate of the magnetic field indicates that the flux rope reached a region where the torus instability was triggered. Conclusions. We conclude that the eruption of this CME was caused by multiple factors, such as photosphere motions, reconnection, and torus instability. Moreover, our simulation successfully reproduced the three-component structures of typical CMEs.