Strong antiferromagnetic (AFM) correlation has long been postulated to be closely related to the occurrence of unconventional high-temperature superconductivity observed in the cuprates, heavy fermions, and organic superconductors. The recently discovered Fe-based superconductors add another interesting member to the list. However, insufficient attention has been paid to the versatile nature of the magnetic correlation in these materials: some showing stripe (C-type) order, others double stripe (E-type) or block AFM order instead, implying potentially richer structures of the superconducting order. Here we report the observation of yet another AFM correlation in the family: a G-type AFM order as seen in the high-T c cuprates, in C u x F e 1 − y As compounds isostructural to the LiFeAs superconductor. This study not only sheds light on the underlying mechanism of the rich magnetic correlations in the Fe-based superconductors, but also suggests the possibility of realizing a distinct pairing symmetry upon chemical doping or applying pressure.