An electronically controlled fixed-frequency beam-scanning periodic leaky-wave antenna operating in a millimeter-wave band is presented in this letter. An air-filled gap waveguide (GW) base is employed as a millimeter-wave excitation thanks to its low-loss property. Totally, 60 patches in a staggered two-row arrangement are introduced as the radiating elements, which get energies from the GW through longitudinal slots etched on the middle metal layer, and this produces reverse phases in the two rows under a TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10</sub> -mode excitation. Then, a method by constructing an equivalent phase constant is developed in this letter, and positive-order-harmonic radiation is used to analyze the radiation property. By introducing the period-reconfigurable method, a fixed-frequency beam-scanning performance is achieved. In addition, the developed antenna is fabricated and experiments have been implemented. A beam-scanning range of 70° from −35° to 35° is realized using the positive-order-harmonic radiations at 29 GHz, and the measured peak gain arrives at 16.5 dBi. The design shows possible applications in millimeter-wave communications.