This research proposes a novel terahertz frequency scanning antenna based on slotted waveguide arrays, and the antenna consisted of 31 elements in a linear array. Usually, the mechanical steering scheme is employed to realize two-dimensional terahertz imaging for most of the systems that inherently have a low frame rate limitation. As an attractive scheme to obtain high frame rate, electrical beam steering by frequency scanning antennas is the preferable approach. Previous scanning waveguide arrays operating on terahertz band cannot suppress sidelobe levels effectively. Thus, to fulfill the requirement of high radiation efficiency, low waveguide loss, and low sidelobe levels, arranging the slots to conform to Taylor distribution was considered. The distributions effectively become frequency-dependent for the beam-steering concept. Compared with the uniform slot distribution, a Taylor distribution ensures broadband radiation patterns with low sidelobe levels. Furthermore, the offset of the slots has been optimized through a power transmission method in combination with full wave simulation. The frequency-controlled beam steering concept and the sidelobe suppression effect were verified by the quasi-optical measurements in the 0.2 THz band. The fabricated slot-array antenna has large angle scanning ability and a low sidelobe property. In addition, the measured scanning range is larger than 50° with a moderate gain of 15 dB over the frequency band 165～215 GHz. The sidelobe levels are remarkably inhibited over 20 dB normalized to the mainlobe level, and the measured radiation patterns and sidelobe suppression effects agree well with HFSS full-wave simulation. The proposed beam-steering antenna has potential applications for THz imaging with a high frame rate.