As a label-free and high-throughput single cell analysis platform, impedance flow cytometry (IFC) suffers from clogging caused by a narrow microchannel as mechanical constriction (MC). Current sheath constriction (SC) solutions lack systematic evaluation of the performance and proper guidelines for the sheath fluid. Herein, we hypothesize that the viscosity of the non-conductive liquid is the key to the performance of SC, and propose to employ non-conductive viscous sheath flow in SC to unlock the tradeoff between sensitivity and throughput, while ensuring measurement accuracy. By placing MC and SC in series in the same microfluidic chip, we established an evaluation platform to prove the hypothesis. Through modeling analysis and experiments, we confirmed the accuracy (error < 1.60% ± 4.71%) of SC w.r.t. MC, and demonstrated that viscous non-conductive PEG solution achieved an improved sensitivity (7.92×) and signal-to-noise ratio (1.42×) in impedance measurement, with the accuracy maintained and free of clogging. Viscous SC IFC also shows satisfactory ability to distinguish different types of cancer cells and different subtypes of human breast cancer cells. It is envisioned that viscous SC IFC paves the way for IFC to be really usable in practice with clogging-free, accurate, and sensitive performance.