Investigated in this paper is a variable-coefficient higher-order nonlinear Schrodinger equation, which can describe the propagation of subpicosecond or femtosecond optical pulse in an inhomogeneous optical fiber. With a set of the Painleve-integrable coefficient constraints, the equation is transformed into its bilinear forms. Single-and two-anti-dark soliton solutions are constructed via the Hirota method. Based on the solutions, we graphically discuss the features of the anti-dark solitons, as well as their interaction, in the inhomogeneous optical fibers. As shown in our results, the backgrounds of the anti-dark solitons are related to the gain/loss coefficients, while the third-order dispersion coefficients directly influence the propagation trajectories of the anti-dark solitons, which provide a possible way to manage these solitons in the inhomogeneous fiber. On the other hand, overtaking interaction between the two anti-dark solitons is obtained, and seen to be elastic. The frequency shift parameter gamma(1) has almost no effect on the solitons.