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Recent learning-based LiDAR odometry methods have demonstrated their competitiveness. However, most methods still face two substantial challenges: 1) the 2D projection representation of LiDAR data cannot effectively encode 3D structures from the point clouds; 2) the needs for a large amount of labeled data for training limit the application scope of these methods. In this paper, we propose a self-supervised LiDAR odometry method, dubbed SelfVoxeLO, to tackle these two difficulties. Specifically, we propose a 3D convolution network to process the raw LiDAR data directly, which extracts features that better encode the 3D geometric patterns. To suit our network to self-supervised learning, we design several novel loss functions that utilize the inherent properties of LiDAR point clouds. Moreover, an uncertainty-aware mechanism is incorporated in the loss functions to alleviate the interference of moving objects/noises. We evaluate our method's performances on two large-scale datasets, i.e., KITTI and Apollo-SouthBay. Our method outperforms state-of-the-art unsupervised methods by 27%/32% in terms of translational/rotational errors on the KITTI dataset and also performs well on the Apollo-SouthBay dataset. By including more unlabelled training data, our method can further improve performance comparable to the supervised methods.