In this work, we develop a very simple batch-learning algorithm for semi-blind extraction of a desired source signal with temporal structure from linear mixtures. A l-though we use the concept of sequential blind extraction of sources and independent component analysis (ICA), we do not carry out the extraction in a completely blind manner neither we assume that sources are statistically independent. In fact, we show that the apriori information about the auto-correlation function of primary sources can be used to extract the desired signals (sources of interest) from their linear mixtures. Extensive computer simulations and real data application experiments confirm the validity and high performance of the proposed algorithm.