This chapter introduces the fast fixed-point algorithms in overdetermined blind source separation in detail, including the fast fixed-point algorithm based on kurtosis and the fast fixed-point algorithm based on negative entropy. The algorithm principle and implementation flow were deduced in detail, and then the multivariate fast fixed-point algorithm and fast fixed-point algorithm for complex signal were introduced. Finally, for speech signal and communication signal, the performances of the fast fixed-point algorithm suitable for real signal and complex signal are simulated and analyzed respectively. The experimental results show that both the fast fixed-point algorithms based on kurtosis and negative entropy have better separation performance.