To address 3D object retrieval, substantial efforts have been made to generate highly discriminative descriptors of 3D objects represented by a single modality, e.g., voxels, point clouds or multi-view images. It is promising to leverage the complementary information from multi-modality representations of 3D objects to further improve retrieval performance. However, multi-modality 3D object retrieval is rarely developed and analyzed on large-scale datasets. In this paper, we propose self-and-cross attention based aggregation of point cloud and multi-view images (SCA-PVNet) for 3D object retrieval. With deep features extracted from point clouds and multi-view images, we design two types of feature aggregation modules, namely the In-Modality Aggregation Module (IMAM) and the Cross-Modality Aggregation Module (CMAM), for effective feature fusion. IMAM leverages a self-attention mechanism to aggregate multi-view features while CMAM exploits a cross-attention mechanism to interact point cloud features with multi-view features. The final descriptor of a 3D object for object retrieval can be obtained via concatenating the aggregated features from both modules. Extensive experiments and analysis are conducted on three datasets, ranging from small to large scale, to show the superiority of the proposed SCA-PVNet over the state-of-the-art methods.