Editing biological sequences has extensive applications in synthetic biology and medicine, such as designing regulatory elements for nucleic-acid therapeutics and treating genetic disorders. The primary objective in biological-sequence editing is to determine the optimal modifications to a sequence which augment certain biological properties while adhering to a minimal number of alterations to ensure safety and predictability. In this paper, we propose GFNSeqEditor, a novel biological-sequence editing algorithm which builds on the recently proposed area of generative flow networks (GFlowNets). Our proposed GFNSeqEditor identifies elements within a starting seed sequence that may compromise a desired biological property. Then, using a learned stochastic policy, the algorithm makes edits at these identified locations, offering diverse modifications for each sequence in order to enhance the desired property. Notably, GFNSeqEditor prioritizes edits with a higher likelihood of substantially improving the desired property. Furthermore, the number of edits can be regulated through specific hyperparameters. We conducted extensive experiments on a range of real-world datasets and biological applications, and our results underscore the superior performance of our proposed algorithm compared to existing state-of-the-art sequence editing methods.