Stress granules (SGs) are highly dynamic cytoplasmic membrane-less organelles that assemble when cells are challenged by stress. At different stages of assembly, various RNA molecules are sorted into SGs where they play important roles in maintaining the structural stability of SGs and regulating gene expression. Despite recent efforts of fluorescence microscopy and biochemical fractionation analysis, there still lacks a complete description of the dynamic changes in the molecular inventory of SG components during different stages of assembly and disassembly. In this study, we applied a proximity-dependent RNA labeling method, CAP-seq, to comprehensively investigate the content of local transcriptome in SGs, in the context of live mammalian cells. CAP-seq captures 457 and 822 RNAs in arsenite- and sorbitol-induced SGs in HEK293T cells, respectively, revealing that SG enrichment is positively correlated with RNA length and AU content, but negatively correlated with translation efficiency. The high spatial specificity of CAP-seq dataset is validated by single-molecule FISH imaging. We further applied CAP-seq profile RNA components in microscopically invisible SG cores, both before stress and after recovery from stress, thus mapping the dynamic changes in SG-proximal transcriptome along the time course of granule assembly/disassembly processes. Our data portray a model of AU-rich and translationally repressed SG nanostructure that are memorized long after the removal of stress.