As a rare transparent conducting oxide material with p-type conductivity, CuAlO₂ can be widely used in fields such as transparent electronic devices and solar cells, but its low conductivity limits its practical applications. In semiconductor materials, there is a direct relationship between the anharmonic effect of phonons and conductivity, which allows for the influence of electrical conductivity by adjusting phonons. However, the anharmonic behavior of phonons in CuAlO₂ is still unclear. In this paper, we prepared CuAl_1-xCr_xO₂ (x=0~0.4) material using a solid-state reaction method and combines X-ray diffraction, Raman scattering spectroscopy, and first principles calculations to study the phonon anharmonic effects of CuAl_1-xCr_xO₂ (x=0~0.4) samples under different pressures and temperatures. The refinement of crystal structure by X-ray diffraction shows that with the increase of Cr doping concentration, the thermal vibration factor of Cu atoms first increases and then decreases, with the maximum thermal vibration factor at x=0.1; Raman scattering spectroscopy and first principles analysis indicate that the E_g and A_1g modes are mainly three phonon processes, but the four phonon process of the A_1g mode increases with increasing doping concentration. Our research results have important guiding significance for further improving the conductivity of CuAlO₂.