This paper addresses the mobility problem in extremely large antenna array (ELAA) communication systems. In order to account for the performance loss caused by the spherical wavefront of ELAA in the mobility scenario, we propose a wavefront transformation-based matrix pencil (WTMP) channel prediction method. In particular, we design a matrix to transform the spherical wavefront into a new wavefront, which is closer to the plane wave. We also design a time-frequency projection matrix to capture the time-varying path delay. Furthermore, we adopt the matrix pencil (MP) method to estimate channel parameters. Our proposed WTMP method can mitigate the effect of near-field radiation when predicting future channels. Theoretical analysis shows that the designed matrix is asymptotically determined by the angles and distance between the base station (BS) antenna array and the scatterers or the user when the number of BS antennas is large enough. For an ELAA communication system in the mobility scenario, we prove that the prediction error converges to zero with the increasing number of BS antennas. Simulation results demonstrate that our designed transform matrix efficiently mitigates the near-field effect, and that our proposed WTMP method can overcome the ELAA mobility challenge and approach the performance in stationary setting.