It is shown by three-dimensional QED particle-in-cell simulation that as a laser pulse of 2.5 PW and 20 fs propagates along a sub-wavelength-wide solid wire, directional synchrotron γ−rays along the wire surface can be efficiently generated. With 8% energy conversion from the pulse, the γ−rays contains 10 12 photons between 5 and 500 MeV within 10 fs duration, corresponding to peak brilliance of 10 27 photons s −1 mrad −2 mm −2 per 0.1% bandwidth. The brilliance and photon energy are respectively 2 and 3 orders of magnitude higher than the highest values of synchrotron radiation facilities. The radiation is attributed to the generation of nC, GeV electron beams well guided along the wire surface and their wiggling motion in strong electrostatic and magnetostatic fields induced at the high-density-wire surface. In particular, these quasistatic fields are so strong that QED effects already play a significant role for the γ−ray radiation. With the laser power P 0 ranging from 0.5 PW to 5 PW available currently, this scheme can robustly produce γ−rays peaked at 1 • with few-mrad divergence and the photon energy and number roughly scales with P 0 and P 3/2 0 , respectively. Our scheme embraces both the merits of high directionality comparable to those based upon laser wakefield acceleration and high charge comparable to those based upon laser-solid interaction.