Lightweight structural alloys have broad application prospects in aerospace, energy, and transportation fields, and it is crucial to understand the hot deformation behavior of novel alloys for subsequent applications. The deformation behavior and microstructure evolution of a new Al-Zn-Mg-Li-Cu alloy was studied by hot compression experiments at temperatures ranging from 300 °C to 420 °C and strain rates ranging from 0.01 s−1 to 10 s−1. The as-cast Al-Zn-Mg-Li-Cu alloy is composed of an α-Al phase, an Al2Cu phase, a T phase, an η phase, and an η′ phase. The constitutive relationship between flow stress, temperature, and strain rate, represented by Zener–Hollomon parameters including Arrhenius terms, was established. Microstructure observations show that the grain size and the fraction of DRX increases with increasing deformation temperature. The grain size of DRX decreases with increasing strain rates, while the fraction of DRX first increases and then decreases. A certain amount of medium-angle grain boundaries (MAGBs) was present at both lower and higher deformation temperatures, suggesting the existence of continuous dynamic recrystallization (CDRX). The cumulative misorientation from intragranular to grain boundary proves that the CDRX mechanism of the alloy occurs through progressive subgrain rotation. This paper provides a basis for the deformation process of a new Al-Zn-Mg-Li-Cu alloy.