In the past few years, the number of space missions with astrophysical purposes has increased, with COROT, KEPLER, MOST and more recently TESS. Two of the most important complementary tools for these missions are the gravity and limb-darkening coefficients, hereafter GDC and LDC. For the missions mentioned above, many calculations are available to be used in several branches of stellar physics: synthetic light curves of eclipsing binaries and planetary transits, stellar diameters, line profiles in rotating stars, etc. see Claret & Bloemen (2011, Cat. J/A+A/529/A75), Claret et al. (2014, Cat. J/A+A/567/A3), Claret (2017, Cat. J/A+A/600/A30) and Claret (2018, Cat. J/A+A/618/A20). However, as noted by Zhou et al. (2018, AJ, submitted), these coefficients are not available for the GAIA mission. The main objective of this Research Note is to provide the theoretical calculations of the LDC and GDC for GAIA. We use two stellar atmosphere models: ATLAS (plane-parallel) and PHOENIX with spherical symmetry (Husser et al. 2013). The specific intensity distribution was fitted using five approaches: linear, quadratic, square root, logarithmic, and a more general one with four terms. These grids cover 19 metallicities ranging from 10^-5^ up to 10^+1^ solar abundances, 0<=logg<=6.0 and 1500K<=Teff<=50000K. The calculations of the gravity-darkening coefficients were performed for all plane-parallel ATLAS models. https://doi.org/10.3847/2515-5172/aaffdf