Next-generation sequencing (NGS) technologies permit the rapid production of vast amounts of data at low cost. Economical data storage and transmission hence becomes an increasingly important challenge for NGS experiments. In this paper, we introduce a new non-reference based read sequence compression tool called SRComp. It works by first employing a fast string-sorting algorithm called burstsort to sort read sequences in lexicographical order and then Elias omega-based integer coding to encode the sorted read sequences. SRComp has been benchmarked on four large NGS datasets, where experimental results show that it can run 5-35 times faster than current state-of-the-art read sequence compression tools such as BEETL and SCALCE, while retaining comparable compression efficiency for large collections of short read sequences. SRComp is a read sequence compression tool that is particularly valuable in certain applications where compression time is of major concern.