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Recent progress in 3D scene understanding has explored visual grounding (3DVG) to localize a target object through a language description. However, existing methods only consider the dependency between the entire sentence and the target object, ignoring fine-grained relationships between contexts and non-target ones. In this paper, we extend 3DVG to a more fine-grained and interpretable task, called 3D Phrase Aware Grounding (3DPAG). The 3DPAG task aims to localize the target objects in a 3D scene by explicitly identifying all phrase-related objects and then conducting the reasoning according to contextual phrases. To tackle this problem, we manually labeled about 227K phrase-level annotations using a self-developed platform, from 88K sentences of widely used 3DVG datasets, i.e., Nr3D, Sr3D and ScanRefer. By tapping on our datasets, we can extend previous 3DVG methods to the fine-grained phrase-aware scenario. It is achieved through the proposed novel phrase-object alignment optimization and phrase-specific pre-training, boosting conventional 3DVG performance as well. Extensive results confirm significant improvements, i.e., previous state-of-the-art method achieves 3.9%, 3.5% and 4.6% overall accuracy gains on Nr3D, Sr3D and ScanRefer respectively.