This paper addresses the mobility problem in massive multiple-input multiple-output systems, which leads to significant performance losses in the practical deployment of the fifth generation mobile communication networks. We propose a novel channel prediction method based on multi-dimensional matrix pencil (MDMP), which estimates the path parameters by exploiting the angular-frequency-domain and angular-time-domain structures of the wideband channel. The MDMP method also entails a novel path pairing scheme to pair the delay and Doppler, based on the super-resolution property of the angle estimation. Our method is able to deal with the realistic constraint of time-varying path delays introduced by user movements, which has not been considered so far in the literature. We prove theoretically that in the scenario with time-varying path delays, the prediction error converges to zero with the increasing number of the base station (BS) antennas, providing that only two arbitrary channel samples are known. We also derive a lower-bound of the number of the BS antennas to achieve a satisfactory performance. Simulation results under the industrial channel model of 3GPP demonstrate that our proposed MDMP method approaches the performance of the stationary scenario even when the users' velocity reaches 120 km/h and the latency of the channel state information is as large as 16 ms.