In the present study, the problem of plane wave diffraction by an impedance half-plane in cold plasma is investigated. The boundary-value problem corresponding to this canonical structure is formulated by Fourier transform technique, and leads to a matrix Wiener-Hopf equation. The resulting matrix is expressed in a form convenient to be factorized by Daniele-Khrapkov method, which yields a formal solution to the problem under consideration. The matrix Wiener-Hopf equation is reduced to a simpler form by assuming epsilon(2) --> 0, where epsilon(2) is an element of the tensor of dielectric permittivity. This occurs; if the operating frequency is assumed very large compared to omega(c) (the cyclotron frequency), while it is at the same order with omega(p) (the plasma frequency), or if the amplitude of the dc magnetic field vector is taken as zero. Asymptotic evaluation of the field integrals yield the high-frequency diffraction coefficients where the field expressions are obtained by the standard saddle-point technique. As a verification of the solution obtained here, it is shown that the expressions for the case epsilon(1) = 1 is identical to the previously obtained results for an impedance half-plane in an isotropic and homogeneous medium.