A uniform asymptotic high-frequency solution is developed for the problem of diffraction of plane waves by a slit in an impedance screen of finite thickness. By using the Fourier transform technique the boundary-value problem is formulated into a pair of simultaneous modified Wiener-Hopf equations of the third kind which are decoupled and solved approximately. Several numerical results illustrating the effects of the surface impedances, slit width and slit thickness on the diffraction phenomenon are presented.