ABSTRACT Most stars are in multiple systems, with the majority of those being binaries. A large number of planets have been confirmed in binary stars and, therefore, it is important to understand their formation and dynamical evolution. We perform simulations to investigate the migration of wide-orbit giant planets (semimajor axis 100 au) in massive circumbinary discs (mass $0.1\, {\rm M}_{\odot }$) that are marginally gravitationally unstable, using the three-dimensional Smoothed Particle Hydrodynamic code seren. We vary the binary parameters to explore their effect on planet migration. We find that a planet in a massive circumbinary disc initially undergoes a period of rapid inward migration before switching to a slow outward migration, as it does in a circumstellar disc. However, the presence of the binary enhances planet migration and mass growth. We find that a high binary mass ratio (binary with equal mass stars) results in more enhanced outward planet migration. Additionally, larger binary separation and/or higher binary eccentricity results to a faster outward planet migration and stronger planet growth. We conclude that wide-orbit giant planets attain wider final orbits due to migration around binary stars than around single stars.