When Levy type rigid bracing dome is impacted by unexpected load, its structure may collapse continuously, resulting in property loss and casualties, therefore, it is necessary to analyze its progressive collapse performance. According to characteristics of rigid bracing dome, the threshold coefficients of members and its calculation formula were given, and the discriminant criteria and types of progressive collapse were proposed. Damage coefficient based on response difference was proposed, and importance coefficient of members was given. Member importance of levy type rigid bracing dome were analyzed and sorted based on importance coefficient of members. Based on the discriminant criteria of progressive collapse and the results of importance analysis of members, the method and process of progressive collapse analysis were proposed. Progressive collapse performance of structure was analyzed. The influence of both rise span ratio and initial prestress on the progressive collapse performance was discussed. The method of progressive collapse resistance against rigid bracing dome was proposed. The research showed that the progressive collapse types of levy type rigid bracing dome could be divided into non collapse, local collapse and overall collapse. The outer ring bar obtains the largest importance coefficient, followed by the inner ring bar. The smaller rise span ratio is or the larger the initial prestress, the smaller importance of the member will be. When the outer ring member, inner ring member or node is damaged, the structure will collapse continuously, while other members will not collapse. Strengthening the joints and ring members can improve resistance of structure against progressive collapse.