Grounding spatial relations in natural language for object placing could have ambiguity and compositionality issues. To address the issues, we introduce ParaGon, a PARsing And visual GrOuNding framework for language-conditioned object placement. It parses language instructions into relations between objects and grounds those objects in visual scenes. A particle-based GNN then conducts relational reasoning between grounded objects for placement generation. ParaGon encodes all of those procedures into neural networks for end-to-end training, which avoids annotating parsing and object reference grounding labels. Our approach inherently integrates parsing-based methods into a probabilistic, data-driven framework. It is data-efficient and generalizable for learning compositional instructions, robust to noisy language inputs, and adapts to the uncertainty of ambiguous instructions.