This brief proposes a design approach for a high-efficiency continuous class-F power amplifier (PA) using quasi-elliptic low-pass filtering matching network (QELMN). In comparison with Chebyshev and modified elliptic matching networks, QELMN is composed of the quasi-elliptic low-pass filter (QEL) and optimized transmission lines (TL). QEL is a harmonic controller and matching circuit with low insertion loss, and its passband can be adjusted for each desired amplifier according to the operating band. Sharp roll-off and wide stopband of QEL controls harmonics, and low insertion loss of QEL improves delivered power from transistor to the load. The input impedance of QELMN is optimized with the goals of the stability and high power-added efficiency. The proposed approach is adopted to implement a continuous class-F PA using an LDMOS device under a class-AB bias condition. Experimental results verify a wide bandwidth from 0.3 to 1 GHz, with measured drain efficiency of 62-81%, the output power of 37-40.3 dBm and power gain of 12-15.3 dB.