  Magneto-electric coupling in pyroelectric CaBaCo$_4$O$_7$ is investigated
using ab-intio calculations and Landau theory. The former shows that
exchange-striction is strong enough to produce a giant change in electric
polarization upon ferrimagnetic ordering, comparable to the experimentally
determined value of ~17 mC/m$^2$ . Furthermore, Landau theory demonstrates that
magneto-elastic coupling in CaBaCo$_4$O$_7$ is responsible for the strong
magneto-electric coupling appearing close to the magnetic phase transition.
