We describe an efficient chemical vapor deposition (CVD) method for synthesizing graphene with a single crystal orientation on the whole surface of a copper (Cu) foil. We specifically synthesized graphene on the inner surface of a folded Cu foil, on which small holes were made for regulating the permeation and adsorption of the gases used for the synthesis. We compared the results of this method, which we call a "hole-pocket" method, with previously developed methods involving traditional synthesis on an open Cu foil and a Cu "pita-pocket". From these comparisons, we found the orientation of recrystallized Cu to depend on the shape of the Cu foil. Our hole-pocket method did not require treatment of the Cu surface with a complicated process to reduce the density of nucleation seeds in order to synthesize large hexagonal graphene grains, nor did it require the use of a single-crystalline substrate because methane passing through holes on the upper side of the hole-pocket slowly decomposed into carbon atoms and the control of the evaporation of Cu inside the foil pocket helped induce a transformation of the Cu domains to Cu(111). The current hole-pocket method resulted in domains that were both large, ranging from 2-5 mm in size, and oriented in the same manner. By extending the synthesis time, we were able to obtain continuous large-area films of single-crystalline orientation on the whole surface with dimensions of several centimeters.