This paper presents a high efficiency push-pull inverse class-F (class-F -1) power amplifier (PA) using a gallium nitride (GaN) transistor for class-S system - a digitally controlled by delta-sigma modulation. To enhance a drain efficiency of class-F -1 PA, the chip-on-board (COB) technique, which can reduce the external parasitic components of the packaged transistor and allow fast switching operation at high frequencies by minimizing distortion of the pulse waveform, is adopted. A harmonic control circuit considering output intrinsic parameters of the transistor from switch-based model controls harmonics to extract pure fundamental frequency of the output signal. For a high efficiency push-pull operation, low loss rat-race baluns are integrated at input and output circuits. From the measured results for a continuous wave of 3.3 GHz, the class-F -1 PA shows a maximum output power of 35.5 dBm and a power gain of about 10 dB. Also, the proposed PA provides a high power-added-efficiency (PAE) of 64.2% and a drain efficiency of 77.2% at maximum output power. The drain efficiency is still remained over 75% in the frequency range of 100 MHz.