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A graphene nanowrinkle (GNW) formed on a Ni substrate, with a width below 5 nm, exhibits a unique feature (van Hove singularities (vHS)) in its electronic structure, owing to the one-dimensional (1D) electron confinement in GNWs. Considering that the 1D electron confinement effect normally appears when the electron motion is isolated in a 1D structure with the insulator-surrounding environment, the experimental observation of vHS in the electronic structure of GNW wedged between metallic graphene sheets has been regarded as extraordinary. Density functional theory calculations were systematically performed and revealed the origin of the 1D quantum confinement in GNW on the Ni substrate, which originated from the crucial role of chemisorption-like interaction between the graphene sheet and Ni surface in spatially separating the π-conjugated state of GNW from that of the graphene sheet. A series of standing waves corresponding to “the 1D particle-in-a-box model” was confirmed by computationally obtained charge densities of GNW. These results demonstrated that the graphene–GNW–graphene on the Ni substrate served a sufficient potential to lead to 1D-electron confinement. Our investigations provide a deeper understanding of the electronic structure in pseudo-1D materials and suggest a novel approach for modulating the electronic structure without chemical modification or complicated etching to break the C–C bond to produce graphene-based 1D nanomaterials, e.g., graphene nanoribbon.