The termination of the Ryukyu trench against Eurasia and the oblique subduction of the Philippine Sea plate create a subduction-collision complex offshore Taiwan, which has not previously been elucidated in detail. We combine traveltime data from the seismic networks in Taiwan and Japan to better illuminate how the subducting Ryukyu slab deforms in this subduction-collision zone. More than 5000 events recorded by both networks were relocated with the double-difference method using an optimal regional one-dimensional velocity model. The offshore seismicity indicates that the double seismic zone, with a gap of 15--20 km, exists in the subducting slab in the depth range of 40--80 km. Focal mechanisms suggest that the double seismic zone is caused by east-west compression resulting from oblique convergence. The improved hypocentral locations for the first time reveal folding of the slab into a horizontal curvature larger in magnitude than and opposite in sign to that of the Ryukyu trench in the depth range 50--100 km. The anomalous curvature, together with the focal mechanisms, suggests that the slab folds against the Eurasian lithosphere and that this deformation cannot be fully elastic. We model this deformation mode as the developing instability of a viscoelastic Maxwell layer embedded in a viscous medium. The characteristic wavelength of the instability, i.e., ~250 km, is consistent with folding of a slab whose viscosity is 100 times higher than that of the surrounding mantle for an along-strike elastic membrane strain as small as 0.01, or more than 3 orders of magnitude higher if 5% elastic strain is allowed.