With the rapid development of wireless communications, GaN HEMT, which has various advantages of high power density, high electron mobility, and high breakdown threshold, receiving increasing attention. Microwave power amplifiers based on GaN HEMTs are widely used in many fields, such as communication, medical, and detection instruments. In the accurate design of GaN microwave power amplifiers, reliable RF large signal model is vitally important. In this paper, a scalable large-signal model based on EEHEMT model is proposed to describe the properties of multifinger AlGaN/GaN high electron mobility transistor (HEMT) accurately. A series of scaling rules is established for the intrinsic parameters of the device, including drain-source current I_ds, input capacitance C_gs and C_gd, which take into account both the gate width of a single finger and the number of gate fingers. With the proposed scalable large-signal model, the performance of the L-band GaN high-efficiency power amplifier with a gate length of 14.4 mm is analyzed. This amplifier demonstrates outstanding performance, with the output power reaching to 46.5 dBm and the drain efficiency arriving at over 70% of the frequency range from 1120 MHz to 1340 MHz. Good agreement between the simulations and experiments is achieved, demonstrating the excellent accuracy of the proposed model. Moreover, the proposed model can further predict the performance of high-order harmonics, providing an effective tool for designing advanced high-power and high-efficiency microwave power amplifiers. Certainly, the EEHEMT model fails to characterize the dynamical behavior induced by trapping and self-heating effects. Thus, for further consideration, scaling models for the thermal resistance and heat capacity need further investigating to broaden the application scope of the proposed model in the case of continuous waves.