Pressure-dependent magnetic properties and magneto-structural phase transitions of the intermetallic Fe2AlB2 compound have been investigated by using spin-polarized density functional theory calculations. From the enthalpy calculations, possible phase transitions are predicted. It is seen that a phase transition from ferromagnetic (FM) to antiferromagnetic (AFM) occurs at 40 GPa, and the other one is from AFM to nonmagnetic (NM) occurs at 96 GPa. To investigate the source of the magneto-structural phase transitions, atomic bonding characteristics, and possible pressure effects on the physical properties of the compound are calculated. And, the structural, electronic, and mechanical properties of FM-, AFM- and NM-phases are considered as a function of pressure on the 0-120 GPa range. Subsequently, the spin-polarized partial and total density of states (DOS), projections of the charge densities, integrated spin densities, magnetization (or net magnetic moment), DOSs at the Fermi level, Mulliken bond overlap populations are studied to present a compact pressure analysis for Fe2AlB2. It is observed that there are sudden changes and discontinuities in the structural and magnetic properties at 40, 54, 59, and 96 GPa pressures as well as the other physical properties, which support the magneto-structural phase transitions.