In 2006-2007, a doublet of M>8 earthquakes occurred in the central segment of the Kuril subduction zone (KSZ), the region with no great earthquakes for a century. Surface displacements observed on the Kuril GPS Array comprise the postseismic transient motion and the interseismic motion at a constant speed. The postseismic motion triggered mostly by the 2006 event prevails in the central third of KSZ, while the interseismic motion caused by subduction prevails in the southwestern and northeastern thirds of KSZ. In the central Kurils, the interseismic deformation is unknown because continuous GPS observations started after the earthquakes. Therefore we model postseismic deformation treating the interseismic component as an additional unknown. Here we analyze the postseismic deformation for four years: 2007.5-2011.5. The observed horizontal deformation with initial velocities to 90 mm/yr can be explained either by viscoelastic relaxation or by afterslip. However, afterslip is not a likely choice for the interval starting 6-8 months after the earthquakes because subsidence is predicted while uplift is observed. We considered three viscoelastic rheologies: Maxwell, Burgers, and standard linear solid (SLS), varying the constant (Maxwell) and transient (Kelvin) viscosities in the range 1 x 10^17 - 1 x 10^20 Pa s. The Maxwell rheology predicts well the observed surface deformation, with the best-fit viscosity 5 x 10^17 Pa s in the asthenosphere. The Maxwell and Burgers rheologies cannot be discriminated in the considered time interval if the constant viscosity is set the same. The SLS rheology is rejected because it predicts the surface deformation an order of magnitude smaller than observed. We used in modeling a spherical layered Earth model and the open-source code VISCO1D of F. Pollitz. The effect of the most prominent aspherical perturbation, the subducting lithospheric slab, was estimated with the open-source code RELAX of S. Barbot. For the model with the slab, the best-fit asthenospheric viscosity must be decreased by a factor of ~2 compared with the spherical layered model. The best-fit Maxwell viscosity in the asthenosphere inferred for KSZ is an order of magnitude smaller than was estimated for several other subduction zones.