The aim of this research is to obtain a composite made of coconut fiber, thermoplastic starch (TPS), ethylene vinyl alcohol (EVOH), and styrene–butadiene copolymer (SBR), achieving the most significant criteria/attribute determined by users. The tools used were quality function deployment (QFD) and the theory of inventive problem solving (TRIZ). The end result indicated that the quality requirement and most representative attribute for users is the toxicity of the material. Four mixtures were made with different percentages of coconut fiber, TPS–EVOH, and SBR, subjecting them to Fourier transform infrared spectroscopy (FTIR), dynamic mechanical analysis (DMA), and thermogravimetric analysis (TGA). The material obtained complies with the requirements of the Food and Drug Administration (FDA) regarding the nontoxicity of synthetic materials (EVOH and SB) to be used in contact with food (packaging and packaging). The spectra IR of the presence of monomers such as methacrylic acid, 2-hydroxyethyl acrylate, itaconic acid, among others, was not detected due to the humidity of the material. On the other hand, the DMA graphs showed that the mixtures achieved high storage modules (from 1500 to 3000 MPa) at temperatures from −90 to −70 °C, and the TGA thermogram showed that the last material to degrade was SBR at temperatures from 400 to 500 °C.