Thermal chemical vapor decomposition of methane on copper is the most widely employed technique for high quality and large area graphene growth. Graphene growth by this technique tends to be limited to a monolayer owing to the surface mediated self-limiting growth mechanism, and hence, it is difficult to obtain continuous bilayers and multilayers. We report the layer-controlled growth of high quality and large area polycrystalline graphene on copper foil in a hot filament chemical vapor deposition (HFCVD) reactor and demonstrate that graphene can be grown with a controlled grain size in the range of 5–16 μm. The field effect hole mobilities of the largest grain monolayer and bilayer graphene and the thickest few-layer graphene are 4310 ± 348, 2745 ± 276, and 2472 ± 185 cm2V–1s–1, respectively, which are comparable to that of high quality polycrystalline graphene and suitable for future nanoelectronics. The results of the systematic parametric study hereby presented indicate that graphene adlayers grow on top of the previously grown layer(s) and show that the HFCVD growth of graphene overcomes the difficulties to growing layer-controlled-graphene on copper. Copper vapor together with carbon radicals produced at the filaments appear to enable the adlayer graphene formation. The versatility and capability of the HFCVD for facile and inexpensive growth of graphene make it a superior technique for industrial applications.