The magnetic exchange behaviour for l-hydroxo and l-acetato double-bridged chromium (III) dimer is investigated based on calculations of density functional theory combined with the broken-symmetry approach. It is demonstrated that there is a magnetic exchange cooperative effect of the two bridging ligands in a double-bridged dimer systems with approximate equal coupling intensity. Meanwhile, the calculated results reveal that the deprotonation of the l-hydroxo ligand causes a sharp increase of the magnetic exchange interaction between the chromium centers. Replacing either the l-hydroxo bridging ligand by one water bridging ligand or the l-acetato bridging ligands by two terminal water ligands produces a relatively reasonable model to examine the contribution on the magnetic exchange interaction of another individual bridging ligand.