Feijoa residues has a high content of bioactive compounds with effective antioxidant activity compared with the content of other fruits. However, these wastes are disposed of without generating added value. Therefore, in order to determine the maximum time to extract the polyphenols (TPC) and flavonoids (TFC) present in the residue, solid-liquid extraction kinetics was performed. Next, in order to find the best conditions for maximizing the simultaneous extraction of TPC and TFC, a central composite design and response surface analysis were proposed. Three independent factors, temperature (ranging from 13.18 to 46.82 °C), solid:liquid ratio (ranging from 1:10 to 1:74 g:mL) and ethanol-water mixture (ranging from 16,36 to 83,64%v/v) were evaluated. The kinetics indicated a maximum extraction time of 90 minutes for TPC with 3,990.02 ± 22.403 mgGAE/100 g FW, and 45 minutes for TFC with 1,219.38 ± 19.24 mgCE/100 g FW. These values are within the range reported by other studies using advanced technology. The optimized extraction conditions were a temperature of 34.5 °C, 1:45 solid-liquid ratio and 39.43% for the solvent. Finally, extract from feijoa residues presented an effective antioxidant activity greater than 50%. Therefore, this residue can be used as a promising source of bioactive compounds with various agro-industrial applications.