We report the first demonstration of group delay tuning with stimulated Raman scattering-induced dispersion in a hydrogen-filled hollow-core optical fiber. A pump laser induces a sharp refractive index change near the S₀(0) Raman transition of hydrogen molecules, enabling the control of the group velocity of signal pulses around the Stokes wavelength. Experiments with an 80-m-long hollow-core fiber filled with 2.5 bar hydrogen achieved continuous tuning of the pulse delay up to 1.42 ns by varying the Raman amplification from 0 to 10 dB. The tunable pulse delay is realized by changing the pump power as well as the hydrogen pressure. This work provides a new technique for controlling the pulse propagation in optical fibers with high flexibility.