Orientation relations between MgO precipitates and Cu matrix have been characterized by electron diffraction. Four orientation relations were newly found to be coincident with Sigma41 [110], Sigma13 [111], Sigma29 [100] and Sigma35 [112] near coincidence-site orientations. The possible dislocation network for these orientation relations was analyzed using O-lattice theory. The size of MgO precipitates with these orientations are in a range of 0.5-1 micron. Frequently appearance of these special orientation relations implies that they may be the favorable orientations for precipitation and coarsening of MgO particles to some extent.