Based on single-phase ac-ac converter with controllable phase and amplitude (ACCPA), a three-phase ACCPA without third harmonic trap was proposed for power transmission control in grid by adopting a symmetrical relationship of three phase. The three-phase ACCPA is comprised of two parts, which are used to adjust the phase and amplitude of three-phase output voltage, respectively, and continuously. Its front part is made up of three buck-type ac converters, and the back part is a three-phase boost-type ac converter. The operation principle of three-phase ACCPA, the adjustable ranges of the phase and amplitude of the front part, and the calculation formulas of control parameters under ideal conditions were studied and deduced in detail. Furthermore, the control accuracy of the phase angle was discussed for the three-phase ACCPA with digital control, and then, the method to select close-loop control parameters was obtained. The control strategy of three-phase ACCPA was presented and a prototype was fabricated. The experimental waveforms and testing results verified the correctness of the theoretical analysis and the feasibility of the control strategy.