The risk assessment of the failure mode of the traditional machining center component rarely considers the topological characteristics of the system and the influence of propagation risks, which makes the failure risk assessment results biased. Therefore, this paper proposes a comprehensive failure risk assessment method of a machining center component based on topology analysis. On the basis of failure mode and cause analysis, considering the correlation of failure modes, Analytic Network Process (ANP) is used to calculate the influence degree of failure modes, and it is combined with component failure mode frequency ratio and failure rate function to calculate independent failure risk. The ANP model of the machining center is transformed into a topological model, and the centrality measurement of network theory is used to analyze the topology of the machining center. The weight of the topological structure index is measured by subjective and objective weighting methods, and then the importance degree of the machining center component is calculated. In this paper, the coupling degree function is introduced to calculate the importance of the connection edge, which is combined with the failure probability to calculate the failure propagation influence degree, and the component propagation failure risk is calculated based on this. Finally, the independent failure risk and the propagation failure risk of the component are integrated to realize the failure risk assessment of the component. Taking a certain type of machining center as an example to illustrate the application, compared with the traditional assessment method, the effectiveness and advancement of the method proposed in this paper have been verified.