The development of next-generation sequencing (NGS) technology presents a considerable challenge for data storage. To address this challenge, a number of compression algorithms have been developed. However, currently used algorithms fail to simultaneously achieve high compression ratio as well as high compression speed. We propose an algorithm STrieGD that is based on a trie index structure for improving the compression speed of FASTQ files. To reduce the size of the trie index structure, our approach adopts a sampling strategy followed by a filtering step using quality scores. Our experiment shows that the compression ratio of our algorithm increased by approx. 50% over GZip, while being nearly equal to that of DSRC. Importantly, the compression speed of the STrieGD is 3 to 6 times faster than GZip and about 55% faster than DSRC. Moreover, with the increase of compressors, the compression ratio remains stable and the compression speed is nearly linear scalable.