The invention discloses a vibration modeling and analyzing method of a crack impeller structure of a centrifugal compressor. The vibration modeling and analyzing method comprises the steps of firstly, providing a modeling method of a centrifugal impeller, obtaining a whole model by rotating and converting a finite element model of a section of the impeller, reducing the DOF (Degree of Freedom) of a system by adopting a hybrid interface modal synthesis method, and simulating a breath effect of a crack by defining a contact mode on a crack interface; secondly, providing a method for solving large-scale symmetrical sparse matrix-inverse matrix, and thus obviously reducing the memory space needed by calculation; finally, providing a method for carrying out statistical analysis on resonant frequency of the crack impeller structure, considering dissonant factors such as manufacturing error and state degradation which exist in an actual impeller, and obtaining statistical regularity of structure resonant frequency under a random dissonant mode. According to the vibration modeling and analyzing method disclosed by the invention, the calculating accuracy is ensured, obvious improvement effect of calculating efficiency is realized at the same time, and a high-efficiency analyzing method is provided for optimal design of the impeller and quantitative diagnosis of the crack.