In this letter, we apply the variational cumulant expansion (VCE) to t
he U(1) LGT with fermion at finite density (mu not equal 0), which has
a complex action. The order parameters L and L at finite temperature
(T not equal 0) are calculated. Our results are compared with MC resu
lts [N. Bilic, H. Gausterer and S. Sanielevici, Phys. Lett. B 198 (198
7) 235] suggesting new conclusions which are different from that of th
e mean field approximation. (C) 1997 Elsevier Science B.V.