Safety analysis of complex systems, such as aero-engines, has always been a challenging problem. In particular, the risk propagation caused by system functional interactions has become increasingly prominent, leading to the difficulty of traditional safety analysis methods. Existing methods are mostly based on manual experience and deduction with difficulty to completely analyze the whole system safety regions. In this paper, a model-based framework is proposed by combining Finite State Machine Network (FSMN) and phase space theory to perform safety analysis of complex systems from function-logic perspective. We first construct the system model and system state-transition network based on FSMN. Then combining with phase space theory, we identify system safety regions of the entire operating space from macro perspective, and investigate the system risk propagation from micro perspective. An aero-engine system is taken as an example to illustrate the proposed method. Our results show that this method has the ability to effectively identify the potential risk factors and explore emergent unknown risks, which can provide guidance for formulating safety testing.