The recent discovery of a large CP violating asymmetry in KL-->pi+pi-e+e- mode has prompted us to seach for the associated KL-->pi 0 pi 0 e+e- decay mode in the KTeV-E799 experiment at Fermilab. In 2.7 x 10(11) K(L) decays, one candidate event has been observed with an expected background of 0.3 event, resulting in an upper limit for the KL-->pi 0 pi 0 e+e- branching ratio of 6.6 x 10(-9) at the 90% C.L.