Joint Space-time Anti-jamming technique has better performance than both space domain processing and time domain processing, but its implementation is difficult due to its computational complexity. With the toeplitz feature of the observation covariance matrix, the covariance matrix to a big toeplitz matrix can be expanded. Based on the new toeplitz matrix and the FFT technique, a fast implementation approach of MSNWF was proposed for joint space-time processing. The comparison result of computation consumption shows that the new approach is efficient, making it easier for the application of joint space-time anti-jamming technique.