The copolymerization of ethylene (E) and cycloolefin (CO) was carried out with rac-Et(Ind)$_2$ZrC $l_2$ and MMAO cocatalyst system to examine the effect of CO structure on catalytic behaviors and properties of copolymer (COC). Various cycloolefins such as norbornene (N), 5-phenyl-2-norbornene (PN) and 5-vinyl-2-norbornene (VN) were used as comonomers. With increasing [CO]/[E] feed ratio, the catalytic activity decreased while the glass transition temperature of copolymer increased. With analysis of the structure of E/VN copolymer by FT-IR and $^{l3}$C-NMR, it was found that the cyclic C=C bond of VN comonomer is selectively polymerized and the vinyl C=C bond remains unreacted. The resulting vinyl C=C bond attached into copolymer provided the functionalization moiety using glycidyl methacrylate.e.