Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schr?dinger equation, since dark solitons can be applied in waveguide optics as dynamic switches and junctions or optical logic devices. Based on the Lax pair, the binary Darboux transformation is constructed under certain constraints, thus the multi-dark soliton solutions are presented. Soliton propagation and collision are graphically discussed with the group-velocity dispersion, third- and fourth-order dispersions, which can affect the solitons'velocities but have no effect on the shapes. Elastic collisions between the two dark solitons and among the three dark solitons are displayed, while the elasticity cannot be influenced by the above three coefficients.