Erbium doped fiber laser (EDFL) is divided into multi- longitudinal mode (MLM) laser and singlelongitudinal mode (SLM) laser according to the frequency domain. The multi-longitudinal mode laser is hard to understand in the field of optical complex systems. Actually, fiber lasers belong to a type of optical complex system with large degree of freedom, hundreds and thousands of longitudinal modes can typically coexist, exhibiting such nonlinear mode dynamics as complex mode hopping and high-dimensional chaos. However, most of the theoretical models and experimental tools for analyzing fiber lasers dynamics only focus on the collective behavior of dense longitudinal modes, omitting the dynamics individual modes, frequency-domain dynamic model for multi-mode fiber lasers is established, in which the quenching effect in ion pairs and the cross coupling mechanism among modes are considered. The multi-mode laser models can effectively describe the individual behavior and clustering behavior of a large number of modes, and reproduce theoretically the multi-mode dynamics of high-dimensional dynamical system in frequency domain.