  We report on a direct lattice calculation of the neutron EDM(NEDM) using the
external electric field method in both quenched and full QCD. In quenched QCD,
we use a $24^3\times 32$ lattice at $\beta=2.6$ with the Iwasaki gauge action
and the clover fermion action to examine the viability of this method. In
particular we investigate possible effects of violation of the periodic
boundary condition of the external electric field on the NEDM signal. We also
study the quark mass dependence of NEDM in quenched QCD, and observe that NEDM
seems to remain non-zero toward the chiral limit because of the quenched
artifact. In 2-flavor full QCD we employ configurations generated by the
CP-PACS collaboration on a $24^3\times 48$ lattice at $\beta=2.1$ with the same
gluon and quark actions as in the quenched case. Since the number of
configurations is limited, we employ 8 different source points per one
configuration and take an average over them. Our preliminary result at three
quark masses ($m_{PS}/m_V\simeq 0.81, 0.76, 0.69$) indicates that non-zero
value for NEDM can be obtained in full QCD. Statistical errors, however, are
still too large to show the theoretically expected behaviour for NEDM in full
QCD that it vanishes in the chiral limit.
