Several methods are studied in order to improve the communication reliability. However, little methods are discussed aim at medium-voltage power line communication (MV-PLC). In this paper, the general idea of the noise elimination based on single-phase line has been changed. There is a new idea to use three-phase line for noise offset. By analysis of the noise correlation properties, the LMS adaptive algorithm is proposed. Simulation and test show that, regular LMS algorithm has high performance, but it is quite sensitive to the abrupt interference of power line noise. In order to resolve this problem, an modified least mean square algorithm gradient adaptive lattice algorithm (GAL) is proposed. The simulations indicate that GAL is able to resist the abrupt interference effectively. It possesses more advantages than regular LMS algorithm and at the same time, it has nearly the same performance to improve the signal-to-noise ration (SNR). With high performance, LMS algorithms are very fit for PLC.