The effect of azimuthal variation of electron density on the surface‐wave propagation along the inner surface of an annular plasma column is described experimentally and analytically. Such inhomogeneity of electron density is induced by the earth's magnetic field, which is not parallel to the direction of electron drift along the column axis. In this case the azimuthal distribution of electric field intensity of the surface wave is distorted, and the dipole mode, which is normally degenerate, splits into two modes with different wave numbers. The field distortion becomes more intense as the inhomogeneity increases and the wavelength decreases. The theoretical analysis shows that the distortion results from the coupling between normal modes by the effect of the inhomogeneity. Experiments are carried out by using a mercury‐vapor‐discharge tube with hot cathode, and the results agree well with the calculations.