This study aimed to improve the functional properties of egg white protein (EWP) by covalent modification of EWP with xanthan gum (XG) and gallic acid (GA)/tannic acid (TA) to form covalent complexes. The structure and functional properties of EWP before and after modification were explored. The results showed that the grafting degree of EWP-GA-XG and EWP-TA-XG reached 37.23% and 44.01% respectively measured by the OPA method. The secondary structure of EWP became loose after reaction with GA/TA and XG, with a decrease in the content of α-helix and an increase in the β-sheet content, thus contributing to the improvement of its functional properties. The DPPH and ABTS radical scavenging rate and iron reduction ability of EWP-GA-XG (44.94%, 56.38%, 18.29 mg VC/μmol) and EWP-TA-XG (85.45%, 88.39%, 39.26 mg VC/μmol) complexes were significantly improved compared with EWP (7.90%, 12.94%, 0.12 mg VC/μmol). The emulsion activity index and emulsion stability index of EWP-GA-XG (10.05 m2/g, 96.43%) and EWP-TA-XG (11.04 m2/g, 96.53%) complexes were also improved as compared to those of EWP (5.94 m2/g, 51.45%). Moreover, the peak transition temperatures of EWP-GA-XG (138.09 °C) and EWP-TA-XG (143.96 °C) complexes were higher than that of EWP (125.00 °C). This study may provide the theoretical basis for improving the functional properties of EWP and expanding its application in the field of food.