Abstract: With the equivalent RLC circuit, the self-inductance of the inductive coupler and the mutual inductance with the cavity of the buncher B1 as a function of the cavity parameters were derived. From the derived equations the required range of the mutual inductance can be determined and a movable coupler has been designed to cover the working frequency range of the buncher properly. The residual inductor and the tuning curve with the coupler are also given.