  The main goal of the work is to study the stochastic averaging principle for
two time-scales stochastic evolution equations driven by L\'evy process. The
solution of reduced equation with modified coefficient is derived to
approximate the slow component of original equation under suitable condition.
It is shown that the slow component can strongly converge to the solution of
corresponding reduced equation in L^p(p>2)-strong convergence sense.Our key and
novelty is how to cope with the changes caused by L\'{e}vy process and higher
order moments.
