Rheological characterization of $TiO_2$ nanoparticle dispersions in polyethylene glycol (PEG 200) is presented over 1-10 wt% particle mass fraction range in terms of shear viscosity, thixotropy and linear viscoelasticity. A stress controlled rheometer fitted by a cone-and-plate system was employed for the rheological measurements between $-10^{circ}C$ and $40^{circ}C$. The non-linear viscoelastic experiments revealed that $TiO_2$-PEG 200 nanofluid exhibits a shear thinning behavior when particle mass fraction exceeds 1%. No appreciable change in the shear viscosity versus shear rate behavior was detected over the course of four days of dispersion storage. At high particle concentrations the dispersions had a yield stress that was determined by fitting the results through Herschel-Bukley model. Within the studied range of particle concentration, no evidence of thixotropic behavior was observed. In addition, relative viscosity measured at high shear region was found to be independent of the temperature. On the other hand, strong temperature dependency was observed at low shear region particularly at high temperatures. Storage and loss moduli of the $TiO_2$-PEG 200 nanofluid were determined by frequency sweep measurements with applied stresses in the linear viscoelastic region. It was found that when the applied stress is lower than the corresponding yield stress $TiO_2$-PEG 200 nanofluid showed a gel structure especially at high particle mass concentration.