In this paper, we propose a new scheme for blind watermarking of three-dimensional (3D) point clouds in the QSplat representation. The proposed watermarking algorithm can support the authentication, the proof of ownership, and the copyright protection of 3D data. We apply the quantization index modulation (QIM) to QSplat position data, such that the quantization indices of points are mapped to either even or odd set according to the watermark. The same watermark is repeatedly embedded into a cluster of the 3D model at a low resolution to guarantee the robustness of the watermark. At the decoder, the watermark is extracted in a blind manner without requiring the original model. Experimental results show that the proposed watermarking algorithm is robust against numerous attacks, including additive random noises, translation, cropping, simplification and their combinations.