3D visual grounding is an emerging research area dedicated to making connections between the 3D physical world and natural language, which is crucial for achieving embodied intelligence. In this paper, we propose DASANet, a Dual Attribute-Spatial relation Alignment Network that separately models and aligns object attributes and spatial relation features between language and 3D vision modalities. We decompose both the language and 3D point cloud input into two separate parts and design a dual-branch attention module to separately model the decomposed inputs while preserving global context in attribute-spatial feature fusion by cross attentions. Our DASANet achieves the highest grounding accuracy 65.1% on the Nr3D dataset, 1.3% higher than the best competitor. Besides, the visualization of the two branches proves that our method is efficient and highly interpretable.