The complete decomposition performed by blind source separation is computationally demanding and superfluous when only the speech of one specific target speaker is desired. In this paper, we propose a computationally efficient blind speech extraction method based on a proper modification of the commonly utilized independent vector analysis algorithm, under the mild assumption that the average power of signal of interest outweighs interfering speech sources. Considering that the minimum distortion principle cannot be implemented since the full demixing matrix is not available, we also design a one-unit scaling operation to solve the scaling ambiguity. Simulations validate the efficacy of the proposed method in extracting the dominant speech.