We present a new model using virial-like equations of state (EOSs) to calculate the viscosity of pure monatomic fluids that are applicable to liquid, gas, and supercritical regions. The viscosity model has been constructed according to the similarity between P-V-T (pressure-volume-temperature) and T--P (temperature-viscosity-pressure) relationship. Over an extensive pressure and temperature ranges, the obtained results are comparable with the experimental data. The average range of application of this model is for reduced temperatures between 0.5 and 43.5 and for reduced pressures between 0.1 and 78.4. The obtained results are consistent with the experimental data, except in the vicinity of the critical point, the average absolute deviation percent is 2.5 compared with the experimental data. Using the temperature and pressure, calculation of fluid viscosity is straightly possible by applying this model. Based on the findings of this paper, prediction of high-pressure liquid and far-supercritical viscosities of a fluid using low-pressure liquid and gaseous EOSs is possible.