This paper presents a new approach for laser linewidth measurement-loss compensated recirculating delayed self-heterodyne interferometer (LC-RDSHI), which is insensitive to the system parameters. Through the derivation of its system output power spectral density function and simulation of beat frequency power spectrum, the characteristics of system parameters insensitivity for proposed method are analyzed and discussed. On this basis, we build the appropriate experimental device and observe the effects of system parameters on the output power spectrum of LC-RDSHI, and we find that the experimental observations agree with theoretical analysis. Besides, based on different experiment system parameters, we make a comparison of linewidth measurements between the proposed method and conventional LC-RDSHI. The results indicate that the system parameters insensitive LC-RDSHI has higher linewidth measurement accuracy, its measurement process is easier, and therefore, it has better application prospects.