This paper proposes a digital Doherty power amplifier (PA) that employs a complex gain compensation mechanism that can be implemented to improve the performance of gallium-nitride (GaN) Doherty PAs. By fully addressing the problems of amplitude misalignment and phase imbalance, which are typically observed at the common junction of the carrier and peaking amplifiers, the proposed complex gain compensation mechanism allows for the recovery of the quasi-ideal load-modulation behavior as well as improvements in the efficiency and output power of the PA. As a result, an average drain efficiency of 50% has been achieved using a one-carrier Worldwide Interoperability for Microwave Access (WiMAX) signal with a peak-to-average power ratio of 7 dB. The complex gain compensation mechanism provided a 5% improvement in the drain efficiency compared to the uneven Doherty PA where only amplitude compensation is employed.