This paper presents for the first time a wideband, continuous quasi-load insensitive Class-E (CQLIE) concept with a novel load network (LN) for wideband Doherty power amplifier (DPA) application. The proposed LN enables proper wideband match to the CQLIE design space impedances at fundamental and harmonic frequencies. Combining with this LN, the CQLIE concept allows to design highly efficient DPAs with low dispersion over wide RF bandwidth and outstanding linearizability for LTE/5G wideband modulated signals of up to 400 MHz. A CQLIE-based GaN DPA prototype targeting 3.4-3.8 GHz has been designed and characterized with pulsed CW of 10% duty cycle, exhibiting 53.5% drain efficiency (DE) at 7.5 dB output back-off power (OBO) of 40.5 dBm over the whole bandwidth. The linearized ACPR of -50.5 dBc and -47.4 dBc using digital predistortion (DPD) for respective 200 MHz and 425 MHz LTE signals proves that the concept is highly beneficial for wideband load modulation architectures.