The indigo dye found in wastewater from printing and dyeing processes is potentially carcinogenic, teratogenic, and mutagenic, making it a serious threat to the health of animals, plants, and humans. Motivated by the growing need to remove indigo from wastewater, this study prepared novel fiber absorbents using melt-blow polypropylene (PP) melt as a matrix, as well as acrylic acid (AA) and maleic anhydride (MAH) as functional monomers. The modification conditions were studied to optimize the double-initiation, continuous-suspension grafting process, and then functional fibers were prepared by melt-blown spinning the modified PP. The results showed that the optimum modification conditions were as follows: a 3.5 wt% interfacial agent, 8 mg/L of dispersant, 80% monomer content, a 0.8 mass ratio of AA to MAH, a 1000 r/min stir speed, 3.5 wt% initiator DBPH grafting at 130 °C for 3 h, and 1 wt% initiator BPO grafting at 90 °C for 2 h. The highest grafting rate of the PP-g-AA-MAH was 31.2%, and the infrared spectrum and nuclear magnetic resonance spectroscopic analysis showed that AA and MAH were successfully grafted onto PP fiber. This modification strategy also made the fibers more hydrophilic. The adsorption capacity of the PP-g-AA-MAH fibers was highly dependent on pH, and the highest indigo adsorption capacity was 110.43 mg/g at pH 7. The fiber adsorption capacity for indigo increased rapidly before plateauing with increasing time or indigo concentration, and the experimental data were well described in a pseudo-second-order kinetic model and a Langmuir isothermal adsorption model. Most impressively, the modified fiber adsorption capacity for indigo remained as high as 91.22 mg/g after eight regeneration and reuse cycles. In summary, the PP-g-AA-MAH fibers, with excellent adsorption-desorption characteristics, could be readily regenerated and reused, and they are a promising material for the removal of indigo from wastewater.