This paper introduces a new method for the frequency response analysis of the structures with nonlinear links. When the local nonlinear structures, especially for the largescale structures, is excited by the harmonic external forces, the describing functions are used to express the nonlinear internal forces. And then the frequency response of the nonlinear system can be expressed by a Quasilinear Receptance Matrix (compared with the Receptance Matrix in the linear system). As the Quasilinear Receptance Matrix is an inverse matrix, an Inverse Matrix Updating (IMU) Method is proposed to transform the highrank inversion problem into lowrank inversion problem. This method makes it much faster to get the frequency responses of the local nonlinear system for largescale structures. Single degree of freedom (SDOF) system and Multidegree of freedom (MDOF) system case studies show that the IMU Method can greatly improve the computational efficiency, and has high calculation stability.