Lower hybrid waves are investigated at the magnetosheath separatrix region in asymmetric guide-field reconnection by using the Magnetospheric Multiscale (MMS) mission. Three of the four MMS spacecraft observe clear wave activities around the lower hybrid frequency across the magnetosheath separatrix, where a density gradient is present. The observed waves are consistent with generation by the lower hybrid drift instability. The characteristic properties of these waves include: (1) the waves propagate toward the x-line in the spacecraft frame due to the large out-of-plane magnetic field, which is in the same direction of the diamagnetic drift of the x-line; (2) the wave potential is about 20\% of the electron temperature. These drift waves effectively produce cross-field particle diffusion, enabling the transport of magnetosheath electrons into the exhaust region. The observations presented in this study indicate unique features of asymmetric guide-field reconnection.