The correlation between the spins of dark matter halos and the large-scale structure (LSS) has been studied in great detail over a large redshift range, while investigations of galaxies are still incomplete. Motivated by this point, we use the state-of-the-art hydrodynamic simulation, Illustris-1, to investigate mainly the spin-LSS correlation of galaxies at a redshift of z = 0. We mainly find that the spins of low-mass, blue, oblate galaxies are preferentially aligned with the slowest collapsing direction (e(3)) of the large-scale tidal field, while massive, red, prolate galaxy spins tend to be perpendicular to e(3). The transition from a parallel to a perpendicular trend occurs at similar to 10(9.4) h(-1) M-circle dot in the stellar mass, similar to 0.62 in the g-r color, and similar to 0.4 in triaxiality. The transition stellar mass decreases with increasing redshifts. The alignment was found to be primarily correlated with the galaxy stellar mass. Our results are consistent with previous studies both in N-body simulations and observations. Our study also fills the vacancy in the study of the galaxy spin-LSS correlation at z = 0 using hydrodynamical simulations and also provides important insight to understand the formation and evolution of galaxy angular momentum.