In source separation based on short-time Fourier transform, asymmetric window functions are useful for low-latency real-time processing because they can reduce the latency while maintaining better separation performance. However, their appropriate design from the viewpoint of source separation performance has not been sufficiently investigated. In this paper, we propose a method for jointly optimizing demixing filters and an asymmetric analysis window within the framework of independent vector analysis (IVA). We represent the analysis window as a weighted sum of bases, which reduces the optimization of the window function to that of a small number of weight parameters. Then, we derive efficient update rules on the basis of the majorization-minimization algorithm. An experiment demonstrated that the proposed method achieves higher separation performance than IVA using a conventional asymmetric window.