The existing works on object-level language grounding with 3D objects mostly focus on improving performance by utilizing the off-the-shelf pre-trained models to capture features, such as viewpoint selection or geometric priors. However, they have failed to consider exploring the cross-modal representation of language-vision alignment in the cross-domain field. To answer this problem, we propose a novel method called Domain Adaptation for Language Grounding (DA4LG) with 3D objects. Specifically, the proposed DA4LG consists of a visual adapter module with multi-task learning to realize vision-language alignment by comprehensive multimodal feature representation. Experimental results demonstrate that DA4LG competitively performs across visual and non-visual language descriptions, independent of the completeness of observation. DA4LG achieves state-of-the-art performance in the single-view setting and multi-view setting with the accuracy of 83.8 % and 86.8 % respectively in the language grounding benchmark SNARE. The simulation experiments show the well-practical and generalized performance of DA4LG compared to the existing methods. Our project is available anonymously at https://sites.google.com/view/da4lg.