We design an all-optical tunable delay line based on both dispersive and wavelength conversion stages involving modulational instability of a two-frequency pump field propagating in a highly birefringent fiber. More precisely, we numerically show that, by varying the frequency separation between the two orthogonally polarized pump waves, we achieve a controllable and continuous delay of hundreds of picoseconds for signal pulse durations from picoseconds to nanoseconds, without pulse distortion and with only small peak power fluctuations. The proposed method does not require any tunable bandpass filter and can be applied to delay digital data streams at tens of Gbit/s depending on the pump power level.