With the maturity of genome sequencing technology, huge amounts of sequence reads as well as assembled genomes are generating. With the explosive growth of genomic data, the storage and transmission of genomic data are facing enormous challenges. FASTA, as one of the main storage formats for genome sequences, is widely used in the Gene Bank because it eases sequence analysis and gene research and is easy to be read. Many compression methods for FASTA genome sequences have been proposed, but they still have room for improvement. For example, the compression ratio and speed are not so high and robust enough, and memory consumption is not ideal, etc. Therefore, it is of great significance to improve the efficiency, robustness, and practicability of genomic data compression to reduce the storage and transmission cost of genomic data further and promote the research and development of genomic technology. In this manuscript, a hybrid referential compression method (HRCM) for FASTA genome sequences is proposed. HRCM is a lossless compression method able to compress single sequence as well as large collections of sequences. It is implemented through three stages: sequence information extraction, sequence information matching, and sequence information encoding. A large number of experiments fully evaluated the performance of HRCM. Experimental verification shows that HRCM is superior to the best-known methods in genome batch compression. Moreover, HRCM memory consumption is relatively low and can be deployed on standard PCs.