Large-scale multiplexing of a fiber Bragg grating (FBG) array with randomly varied characteristic parameters (RVCPs) is proposed. The center wavelength of each FBG and the grating spacing between adjacent FBGs are randomly varied within a controlled range. Due to the low reflectivity (<-45 dB) and RVCPs of the FBGs, the sensing array presents low spectral-shadowing crosstalk and multiple-reflection crosstalk, implying high FBG multiplexing capacity. The numerical and experimental results show that the RVCP-FBG array significantly improves the signal-to-noise ratio and demodulation accuracy of the distributed sensing system. Large-scale multiplexing of 10,000 FBGs along a 10 m long fiber is achieved.