Aiming at the problem of delay estimation for singlechannel mixed signals, an algorithm based on recursive least squares (RLS) is proposed, which divides the delay estimation into coarse estimation based on cyclic statistics and fine estimation based on RLS, using the timeaveraged criterion of power of two to iteratively update the rough estimate of time delay to complete the entire estimation process. The algorithm has a simple structure, fast convergence speed, and obvious improvement in estimation accuracy, but it is more dependent on the delay difference of the two signals. Simulation experiment results prove the effectiveness of the algorithm.