The separation of signals with temporal structure from mixed sources is a challenging problem in signal processing. For this problem, blind source extraction (BSE) is more suitable than blind source separation (BSS) because it has lower computation cost. Nowadays many BSE algorithms can be used to extract signals with temporal structure. However, some of them are not robust because they are too dependent on the estimation precision of time delay; some others need to choose parameters before extracting, which means that arbitrariness can't be avoided. In order to solve the above problems, we propose a robust source extraction algorithm whose performance doesn't rely on the choice of parameters. The algorithm is realized by maximizing the objective function that we develop based on the non-Gaussianity and the temporal structure of source signals. Furthermore, we analyze the stability of the algorithm. Simulation results show that the algorithm can extract the desired signal from large numbers of observed sensor signals and is very robust to error in the estimation of time delay.