The emergence of microfluidic droplets offers new opportunities to advance biomedical engineering, food production, and energy storage applications. These applications always involve complex fluids exhibiting obvious non-Newtonian behavior. Droplet generation has been extensively addressed, while the complete understanding of droplet generation in non-Newtonian fluid system is still nascent. Here, we present the study of non-Newtonian droplet generation in a flow-focusing microchannel. Polyethylene oxide aqueous solutions are used as the dispersed phase, while olive oil serves as the continuous phase to induce the generation. The molecular weight of polymer is constant while the concentrations are varied from dilute to semi-dilute regimes that are rarely explored in existing studies. The main features of non-Newtonian droplet generation are first identified, after which the concentration-dependent dripping to jetting transitions are clarified. The effects of shear thinning and elasticity on droplet generation are then separately investigated. We finally propose a scaling relation to predict the primary droplet size with the satellite droplets neglected. These results can not only extend the fundamental theory of droplet microfluidics but also facilitate the practical applications.