Microfluidics-based technologies have attracted much attention since the fluid flow can be controlled precisely and only small sample volumes are required. Viscoelastic non-Newtonian fluids such as polymer solution and biofluids are frequently used in microfluidic analyses, and it is essential to understand the small-scale flow dynamics of such viscoelastic fluids. In this work, we report on vortex generation at the junction region of a flow-focusing microchannel, where a central flow stream of a Newtonian fluid meets two sheath flows of a non-Newtonian poly (ethylene oxide) aqueous solution. We elucidated the vortex-generation mechanism by the backward-flow component induced by the first normal stress difference in the viscoelastic sheath fluid. We systematically investigated the effects of polymer concentration, total flow rate, and total to central-stream flow-rate ratio, on the vortex generation. In addition, we demonstrated that this phenomenon can be engineered to enhance the mixing in the flow-focusing microchannel. We expect this work to be helpful for the understanding of viscoelastic flow dynamics in microscale flows and also for the development of microfluidic mixers.