Abstract：A multi-dimensional vector radix Fast Fourier Transform (FFT) algorithm with Decimation In Frequency (DIF) was proposed. Using vector radix 2 DIF for each dimension of the multi-dimensional frequency domain signal, the general form of butterfly computation of the FFT algorithm was obtained. This FFT algorithm can be used with arbitrary integer dimensions. For 1-dimension, the algorithm will be simplified as the well-known DIF vector radix 2 FFT. To facilitate the programming, flow chart with DIF 3-dimension vector radix FFT was given. And this flow chart can be extended to any integer dimensions easily. The comparison results show that, compared with multi-dimensional separable FFT, the DIF multi-dimensional vector radix FFT algorithm has lower calculation load.