  By using the $\Phi$-entropy inequality derived in \cite{Wu, Ch} for Poisson
measures, the same type of inequality is established for a class of stochastic
differential equations driven by purely jump L\'evy processes. The semigroup
$\Phi$-entropy inequality for SDEs driven by Poisson point processes as well as
a sharp result on the existence of invariant probability measures are also
presented.
