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We propose HEARTSVG, a distribution-free, test-based method for fast and accurately identifying spatially variable genes in large-scale spatial transcriptomic data. Extensive simulations demonstrate that HEARTSVG outperforms state-of-the-art methods with higher\n \n \n $${F}_{1}$$<\/jats:tex-math>\n \n \n \n F<\/mml:mi>\n <\/mml:mrow>\n \n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n scores (average\n \n \n $${F}_{1}$$<\/jats:tex-math>\n \n \n \n F<\/mml:mi>\n <\/mml:mrow>\n \n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n Score=0.948), improved computational efficiency, scalability, and reduced false positives (FPs). Through analysis of twelve real datasets from various spatial transcriptomic technologies, HEARTSVG identifies a greater number of biologically significant SVGs (average AUC\u2009=\u20090.792) than other comparative methods without prespecifying spatial patterns. 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