For Class-E/F3 power amplifiers (PAs) working in the radio frequency (RF) band, the freedom of broadband design is limited because the original design space is a single point. In this paper, a new bandwidth-extended Class-E/F3 PA is proposed, which is based on finite harmonic tuning and continuous mode design philosophy. In the theoretical derivation, the high-efficiency frequency domain equations are solved in conjunction with the inherent conditions of the transistor, resulting in a waveform cluster that can expand the design space while keeping the efficiency constant. This approach eliminates the need for tedious circuit derivation and is able to allow greater design freedom. With the extended Class-E/F3 design space, a broadband PA using GaN HEMT CGH40010F operating in the bandwidth of 1.9–3.3 GHz is designed and tested. The experimental results show that the designed PA demonstrates 65% to 74.8% drain efficiency (DE) and 40.1 to 41.7dBm output power over the target bandwidth.