The GRAVITY instrument installed at VLTI uses differential fibered delay lines to spatially filter the incoming wavefronts and accurately control the optical path difference between the Fringe Tracker (FT) and Scientific Detector (SC) parts of the instrument. On top of the differential dispersion occurring in the air, the chromatic dispersion introduced by these fibers impacts the real time performances of the fringe tracker by generating a second-order chromatic phase shift. Moreover, differential dispersion also affects GRAVITY dual-feed measurements that require a length adjustment of both FT and SC fibers. In this contribution, we show how chromatic dispersion can be corrected both in the fringe tracker real-time control as well as in the astrometric data reduction.