Based on the traditional multi-wavelength iterative algorithm, we introduce the angular spectrum transmission theory and the gradient acceleration function, and present a fast convergent phase restoration iterative algorithm, namely, the multi-wavelength gradient acceleration phase retrieval iterative algorithm. The algorithm uses the light field intensity information detected at a fixed position when the light sources with different wavelengths go through the same light path. Through iterative approximation and by introducing the gradient acceleration function in the iterative process, the convergence speed is improved, and the input phase information is recovered. The simulation model is built, the initial iteration value is selected randomly, the input field for a known phase distribution is recovered, and the result is compared with that of the traditional multi-wavelength iteration algorithm. The relative root mean square value, which represents the phase plane reconstruction accuracy of the algorithm, achieves 10-3 orders of magnitude. Convergence rate is increased by more than two times. In the contrast experiments, multiple sets of light sources with different wavelength number within 635 nm to 785 nm are selected. The results show the method has good fast convergence and high precision phase retrieval ability when the wavelength number is 7 and 8.