Generation and propagation of lower hybrid drift wave (LHDW) near the electron diffusion region (EDR) during guide field reconnection at the magnetopause is studied with data from the Magnetospheric Multiscale mission and a theoretical model. Inside the current sheet, the electron beta (β e) determines which type of LHDW is excited. Inside the EDR, where the electron beta is high (β e ∼ 5), the long-wavelength electromagnetic LHDW is observed propagating obliquely to the local magnetic field. In contrast, the short-wavelength electrostatic LHDW, propagating nearly perpendicular to the magnetic field, is observed slightly away from the EDR, where β e is small (∼0.6). These observed LHDW features are explained by a local theoretical model, including effects from the electron temperature anisotropy, finite electron heat flux, electrostatics, and parallel current. The short-wavelength LHDW is capable of generating significant drag force between electrons and ions. Plain Language Summary The lower hybrid drift wave (LHDW) is generated inside the current sheet by the electric current perpendicular to the local magnetic field. With data from the Magnetospheric Multiscale (MMS) mission, we confirm that two types of LHDW are excited in the current sheet during magnetic reconnection with guide field, depending on the local plasma parameter, called beta (ratio between the magnetic field pressure and plasma pressure). One is the short-wavelength, quasi-electrostatic LHDW excited just outside the central reconnection site, called the electron diffusion region. The other is the long-wavelength, electromagnetic LHDW excited in the electron diffusion region. A local theoretical model is developed to explain the excitation of both types of the LHDW in the current sheet. Results from the model agree with MMS observations. The short-wavelength LHDW is capable of generating additional friction between electrons and ions, indicating possible importance of this LHDW on reconnection and electron dynamics.