Recently, researches on resource-saving mixed-radix Fast Fourier Transform(FFT) technology with low complexity and high efficiency are of vital importance in digital signal processing. In this paper, a new mixed-radix FFT decomposition algorithm based on Field Programmable Gate Array(FPGA) is proposed and implemented. The proposed in-place algorithm adopts a hybrid decomposition mode combining prime factorization algorithm and Cooley-Tukey algorithm, which can save one-step multiplication operation of the rotation factor and also reduce the storage space and operation amount effectively, while it also uses the universal butterfly unit module to accommodate to the radix-2, radix-3, and radix-4 FFT operations. The simulation results indicate that the proposed algorithm can greatly improve the flexibility of FFT processing points and effectively save computing resources.