Abstract Deoxyribonucleic acid (DNA) or ribonucleic acid (RNA) sequence compressors for novel species frequently face challenges when processing wide-scale raw, FASTA, or multi-FASTA structured data. For years, molecular sequence databases have favored the widely used general-purpose Gzip and Zstd compressors. The absence of sequence-specific characteristics in these encoders results in subpar performance, and their use depends on time-consuming parameter adjustments. To address these limitations, in this article, we propose a reference-free, lossless sequence compressor called GraSS (Grammatical, Statistical, and Substitution Rule-Based). GraSS compresses sequences more effectively by taking advantage of certain characteristics seen in DNA and RNA sequences. It supports various formats, including raw, FASTA, and multi-FASTA, commonly found in GenBank DNA and RNA files. We evaluate GraSS’s performance using ten benchmark DNA sequences with reduced number of repeats, two highly repetitive RNA sequences, and fifteen raw DNA sequences. Test results indicate that the weighted average compression ratios (WACR) for DNA and RNA sequences are 4.5 and 19.6, respectively. Additionally, the entire DNA sequence corpus has a total compression time (TCT) of 246.8 seconds (s). These results demonstrate that the proposed compression method performs better than several advanced algorithms specifically designed to handle various levels of sequence redundancy. The decompression times, memory usage, and CPU usage are also very competitive. Contact: anirban@klyuniv.ac.in