3D point clouds associated with attributes are considered as a promising paradigm for immersive communication. However, the corresponding compression schemes for this media are still in the infant stage. Moreover, in contrast to conventional image/video compression, it is a more challenging task to compress 3D point cloud data, arising from the irregular structure. In this paper, we propose a novel and effective compression scheme for the attributes of voxelized 3D point clouds. In the first stage, an input voxelized 3D point cloud is divided into blocks of equal size. Then, to deal with the irregular structure of 3D point clouds, a geometry-guided sparse representation (GSR) is proposed to eliminate the redundancy within each block, which is formulated as an ℓ0-norm regularized optimization problem. Also, an inter-block prediction scheme is applied to remove the redundancy between blocks. Finally, by quantitatively analyzing the characteristics of the resulting transform coefficients by GSR, an effective entropy coding strategy that is tailored to our GSR is developed to generate the bitstream. Experimental results over various benchmark datasets show that the proposed compression scheme is able to achieve better rate-distortion performance and visual quality, compared with state-of-the-art methods.