Spatially resolved transcriptomics have enabled the inference of gene expression patterns within two and three-dimensional space, while introducing computational challenges due to growing spatial resolutions and sparse expressions. Here, we introduce scBSP, an open-source, versatile, and user-friendly package designed for identifying spatially variable genes in large-scale spatial transcriptomics. scBSP implements sparse matrix operation to significantly increase the computational efficiency in both computational time and memory usage, processing the high-definition spatial transcriptomics data for 19,950 genes on 181,367 spots within 10 seconds. Applied to diverse sequencing data and simulations, scBSP efficiently identifies spatially variable genes, demonstrating fast computational speed and consistency across various sequencing techniques and spatial resolutions for both two and three-dimensional data with up to millions of cells. On a sample with hundreds of thousands of sports, scBSP identifies SVGs accurately in seconds to on a typical desktop computer.