We investigate the electronic and magnetic properties of the new compound Gd2Co2Al by using a self-consistent full-potential linearized augmented plane-wave method within the local spin-density approximation (LSDA) and the LSDA+U approximation to the exchange-correlation potential of the spin-density functional theory. We have also discussed the reason of system to have low Curie temperature, and made use of the average field theory to calculate the Curie temperature in combination with the results of density functional calculation. Our calculation shows that this system is a metallic conductor. The local Gd magnetic moment provides predominately the strong ferromagnetism and the Co-site local moment is unstable. Gd2Co2Al is shown to be a ferrimagnetic phase due to the moment of Gd sublattice being aligned antiparallelly to the Co moment in the LSDA. After considering the on-site Coulomb interaction by an additional Hubbard parameter U, it is found that the ground state becomes ferromagnetic at a moderate value of U (3.0eV), with a Co ion magnetic moment of 0.024μB, which is in good agreement with experiment. The moment of Co changes much and the density of states of Gd and Co are significantly redistributed with the change of U, while the magnetic moment of Gd does not change much. The competition of 5d-3d hybridization and the on-site Coulomb interaction leads to the fluctuation of the moment of Co.