Abstract In the past decades, both the increasing experimental evidences and some results of theoretical investigation on non-Kolmogorov turbulence have been reported. This has prompted the study of optical propagation in non-Kolmogorov atmospheric turbulence. In this paper, using a non-Kolmogorov power spectrum which owns a generalized power law instead of standard Kolmogorov power law value 11/3 and a generalized amplitude factor instead of constant value 0.033, the fiber-coupling efficiency of plane and spherical waves are derived for horizontal link in weak turbulence. The analytic expressions are obtained and then used to analyze the effect of spectral power-law variations on the fiber-coupling efficiency. It is anticipated that this work is helpful to the investigations of atmospheric turbulence and optical wave propagation in the atmospheric turbulence.