In the present work, polycrystalline Co52V29+Ga-x(19-x)(0 <= x <= 2) Heusler alloys have been prepared. The related experimental results confirm that each sample undergoes a first-order martensitic transformation (MT) from the L2(1) cubic austenitic state to the D0(22) tetragonal martensitic state. With increase of V concentration, both transformation temperature and strain are heightened simultaneously, thus giving rise to an increment of transition entropy change (Delta S-tr). In addition, the influence of hydrostatic pressure on MT and transition strain have been also carefully studied. With increase of pressure, the transformation temperatures of these samples move to high values apparently, but their reversible strain only exhibit a slight enhancement and quickly approach the saturated values. For different compositions, however, there is no obvious difference in the rate of transformation temperature change with pressure. Such a behavior opens up the potential applications of the functional properties associated with the hydrostatic pressure-induced MT for this system.