Polymer nanofibers can be generated by a electrospinning process. The process involves electrically charged jet of polymer solutions evolving from a droplet. The jet stretches in vertical direction due to the difference between charged particle and constant current located at the collector, while the Coulomb and viscoelastic forces start to contribute to radial and azimuthal (torsional) stretching. In this paper, the unstable dynamics of the liquid polymer jet is examined experimentally and theoretically. A complex viscoelastic rheological model has been adopted to analyze the behavior of a charged liquid jet. The model includes complex phenomena of stress relaxation of the liquid jet resulting from the competing force components. The experimental data of the jet paths captured by high-speed videocamera also confirm the similar behavior with the predictions.