Understanding of thermophysical and transport properties of H2-NG blends are needed for the gradual introduction of hydrogen into the national gas grid. A capillary tube viscometer was used to measure the viscosity of hydrogen + methane blends (with hydrogen mole fraction = 0, 0.1000, 0.1997, 0.5019, and 1) at temperatures from 213 to 324 K and pressures up to 31 MPa. A total 147 experimental viscosity measurements were made for the three H2 + CH4 blends and compared against the predictions of five different viscosity models: a one-reference corresponding states (Pedersen) model, a two-reference corresponding states (CS2) model, an extended corresponding states (ECS) model, a corresponding states model derived from molecular dynamic simulations of Lennard Jones (LJ) fluids, and a residual entropy scaling (SRES) method. All the model predictions showed a relatively low deviation compared to the measured viscosities. The density required for viscosity model predictions were computed using Multi-Fluid Helmholtz Energy Approximation (MFHEA) equations of state (EoS). To check the experimental procedure and applicability of the viscometer equipment, viscosity validation measurements were carried out for propane, hydrogen, and methane. The measured viscosities of the pure components were in good agreement with the respective viscosity models with AARD of 0.24%, 0.25%, and 0.58% for propane, hydrogen, and methane, respectively.