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Transfer-free graphene growth via annealing-induced carbon segregation was investigated on a series of carbon/metal/silica layered samples prepared by sequential deposition of Ni from evaporation of Ni and amorphous carbon thin layers from carbon fiber threads on different silica substrates and further thermal treatments with different annealing times, in an attempt to clarify the evolution of carbon formation and its structural variation along with the segregation procedure. Raman and X-ray photoelectron spectroscopies were applied to analyze the microstructure and chemical composition of the generated graphene layer and the carbon microstructure in the depth direction of the metal layer with the aid of Ar-ion etching. The results revealed the annealing-time dependence of the generated graphene quality, possibly because of the competition between carbon diffusion and metal carbide formation/decomposition during annealing. Few-layer stacked graphene sheets with lower defect concentration and larger crystalline size could be grown with increasing annealing time (<1.5 h), while further extending the annealing time resulted in the pronounced formation of amorphous carbon. Similar results were obtained on different types of silica substrates, revealing that growth of graphene was conspicuously independent of the type of the silica substrate, despite a slight difference in the obtained graphene quality owing to a difference in the lattice microstructure and the surface defect. The in-depth understanding of the mechanism of graphitization helps further development of direct growth of high-quality graphene on insulating substrates for applications in electronic devices.