<p>In this paper, we investigate the generalized high-order coupled nonlinear Schrödinger system with modulating coefficients which is used to describe the optical pulses in inhomogeneous media. This work makes two fundamental advances: first, we rigorously derive the Hirota bilinear representation of this system, previously unreported in the literature; second, we use a novel parameter truncation method that enables to obtain the non-degenerate soliton solutions. Specifically, non-degenerate one-, two-soliton solutions are successfully obtained for the first time. Based on inference, we obtain the forms of non-degenerate <i>N</i>-soliton solutions for this system. In addition, by controlling high-order dispersion and self-steepening shift effect, <i>u</i>-shape, <i>v</i>-shape, <i>w</i>-shape, and other shapes of double-hump figures can also be provided. Finally, after selecting appropriate parameters, we analyse the dynamic behaviors of non-degenerate solitons during collisions.</p>