With the rapid development of high integrations in large complex systems, such as aircraft, satellite, and railway systems, due to the increasingly complex coupling relationship between components within the system, local disturbances or faults may cause global effects on the system by fault propagation. Therefore, there are new challenges in safety analysis and risk assessment for complex systems. Aiming at analyzing and evaluating the inherent risks of the complex system with coupling correlation characteristics objectively, this paper proposes a novel risk assessment and analysis method for correlation in complex system based on multi-dimensional theory. Firstly, the formal description and coupling degree analysis method of the hierarchical structure of complex systems is established. Moreover, considering the three safety risk factors of fault propagation probability, potential severity, and fault propagation time, a multi-dimensional safety risk theory is proposed, in order to evaluate the risk of each element within the system effecting on the overall system. Furthermore, critical safety elements are identified based on Pareto rules, As Low As Reasonably Practicable (ALARP) principles, and safety risk entropy to support the preventive measures. Finally, an application of an avionics system is provided to demonstrate the effectiveness of the proposed method.