A class-F high efficiency GaN power amplifier (PA) for dual band operation at 2.14GHz and 2.35GHz is proposed. A novel dual band harmonic-rejection load network, which controls the terminating impedances of the second and third harmonics, and contributes greatly to efficiency improvement of PA, is described. In addition, a matching network which guarantees the high efficiency and gain of PA for the desired dual bands is designed. The proposed load network has the harmonic rejection of more than 24dB which is sufficient for rejecting harmonics, and an insertion loss of less than 0.11dB. The dual band matching network for the maximum output power results in the measured highest output power for each operating frequency. The fabricated class-F GaN PA has 43dBm-65.4% and 43dBm-63.9% of output power - efficiency at the desired dual frequencies.