  We investigate the flavour changing neutral currents (FCNC) generated by
dimension six four-fermion operators at the Large Hadron-Electron Collider
(LHeC) proposed at CERN in an effective approach. This is performed by monte
carlo analysis at the full detector level, as the background is successfully
reduced by using invariant mass scheme to require the final states to
reconstruct the mass (transverse mass) of the top quark (W boson). Our analysis
shows that the future electron proton colliders like the LHeC can probe
competitive limits for the top FCNC dimension six four fermion operators such
as $C_{lq}^{(1)ee31} < 0.0647$, $C_{lu}^{ee31} < 0.109$, $C_{lequ}^{(1)ee31} <
0.217$ and $C_{lequ}^{(3)ee31} < 0.0209$ in the Warsaw basis.
