Estimation of lithospheric viscosity remains challenging, especially for variations with spatial scales less than 100 km. Some recent studies have developed a method to determine viscosity structure from electrical conductivity models determined from magnetotelluric (MT) data. This method was initially applied to the extensional transition zone from the Great Basin to Colorado Plateau. Here, we use this approach to infer the effective lithospheric viscosity in a convergent setting by using an MT profile that crosses the eastern margin of the Tibetan Plateau. The profile extends from the Songpan-Ganzi block, crosses the 2008 Wenchuan earthquake epicenter region and ends in the Sichuan basin. The preferred viscosity structure is characterized by the middle-lower crustal viscosities in the range 2.42 × 10^18–2.69 × 10²¹ Pa⋅s below the Songpan-Ganzi block. In the Longmenshan fault zone and 2008 Wenchuan Ms8.0 earthquake area, the crustal viscosity is higher and in the range 4.32 × 10^18–5.10 × 10²¹ Pa⋅s with significant small-scale (< 100 km) lateral variations. The MT-derived viscosities are consistent with previous regional-scale estimates but reveal the viscosity structure in more detail. The preferred geodynamic model can explain both the crustal deformation velocity and the small-scale lateral variations of surface topography. It implies that the crustal deformation is driven by mantle flow that results in a weak coupling of the upper and middle-lower crust beneath the eastern Tibetan Plateau. The inferred viscosity structure may help further understand the earthquake mechanisms in the Longmenshan fault zone.