Sodium-ion batteries are economical and environmentally sustainable energy storage batteries. Among them, β-NaMnO₂, a promising sodium-ion cathode material, is a manganese-based oxide with a corrugated laminar structure, which has attracted significant attention due to its structural robustness and relatively high specific capacity. However, it has short cycle life and poor rate capability. To address these issues, Ti atoms, known for enhancing structural stability, and Cu atoms, which facilitate desodiation, were doped into β-NaMnO₂ by first-principles calculation and crystal orbital Hamilton population (COHP) analysis. β-NaMn_0.8Ti_0.1Cu_0.1O₂ exhibits a notable increase in reversible specific capacity and remarkable rate properties. Operating at a current density of 0.2C (1C = 219 mA·g^-1) and within a voltage range of 1.8-4.0 V, the modified material delivers an initial discharge capacity of 132 mAh·g^-1. After charge/discharge testing at current densities of 0.2C, 0.5C, 1C, 3C, and 0.2C, the material still maintains a capacity of 110 mAh·g^-1. The doping of Ti atoms slows down the changes in the crystal structure, resulting in only minimal variation in the lattice constant c/a during the desodiation process. Mn and Cu engage in reversible redox reactions at voltages below 3.0 V and around 3.5 V, respectively. The extended plateau observed in the discharge curve below 3.0 V signifies that Mn significantly contributes to the overall battery capacity. This study provides insights into modifying β-NaMnO₂ as a cathode material, offering experimental evidence and theoretical guidance for enhancing battery performance in Na-ion batteries.