Surface wrinkles in homogeneous and heterogeneous film-substrate systems have received intense attention in both science and engineering. Understanding the wrinkling phenomena of heterogeneous systems with continuously variable features is still a challenge. In this work, we propose an unconventional strategy to prepare periodic thickness-gradient metal films on polydimethylsiloxane (PDMS) substrates by masking of copper grids which are weaved by orthometric copper wires. It is found that a periodic thickness-gradient film spontaneously forms during the sputtering process because of the specific structures of the copper grids. Surface wrinkles are strongly modulated by the copper grid structures and are position-dependent within a period. A phase diagram has been established to correlate the wrinkle morphology with the mesh size and film thickness. The film surfaces at mesh centers are evolved from labyrinth wrinkling to herringbone wrinkling and then to stripe wrinkling and finally to wrinkling-free state when the mesh size decreases and/or the film thickness increases. The morphological characteristics, evolutional behaviors, and underlying mechanisms of such wrinkling are discussed in detail based on the stress theory and numerical simulation.