The electronic, Fermi surface (FS) and magnetic properties of ferromagnetic Heusler alloys Co2XY (X = Cr, Mn, Fe; Y=Al, Ga) have been investigated by means of first principles calculation. Out of these compounds, Co2CrAl is found to be perfectly half-metallic (HM) at ambient. Under pressure HM to nearly HM (NHM) transition is observed around 75 GPa for Co 2CrAl and NHM to HM transition is observed around 40 GPa and 18 GPa for Co2CrGa and Co2MnAl, respectively, while no transition is observed for other compounds under study and is also analyzed from the FS studies. The states at the Fermi level in the majority spin are strongly hybridized Co-d and X-d like states. The majority band FS topology change is observed under pressure for the compounds where we observe a transition, while the minority band FS remain unaltered under pressure for all compounds except in Co2FeGa, where we observed an electron sheet at X point instead of hole pocket at Γ point. © 2013 American Institute of Physics.