Earth’s inner core anisotropy is widely used to infer the deep Earth's evolution and present dynamics. Many compressional-wave anisotropy models have been proposed based on seismological observations. In contrast, inner-core shear-wave (J-wave) anisotropy – on a par with the compressional-wave anisotropy – has been elusive. Here we present a new class of the J-wave anisotropy observations utilizing earthquake coda-correlation wavefield. We establish that the coda-correlation feature I2-J, sensitive to J-wave speed, exhibits time and amplitude changes when sampling the inner core differently. J-waves traversing the inner core near its center travel faster for the oblique than equatorial angles relative to the Earth’s rotation axis by at least ~5 s. The simplest explanation is the J-wave cylindrical anisotropy with a minimum strength of ~0.8%, formed through the lattice-preferred-orientation mechanism of iron. Although we cannot uniquely determine its stable iron phase, the new observations rule out one of the body-centered-cubic iron models.