In this paper, we propose a new online independent vector analysis (IVA) algorithm for real-time blind source separation (BSS). In many BSS algorithms, the iterative projection (IP) has been used for updating the demixing matrix, a parameter to be estimated in BSS. However, it requires matrix inversion, which can be costly, particularly in online processing. To improve this situation, we introduce iterative source steering (ISS) to online IVA. ISS does not require any matrix inversions, and thus its computational complexity is less than that of IP. Furthermore, when only part of the sources are moving, ISS enables us to update the demixing matrix flexibly and effectively so that the steering vectors of only the moving sources are updated. Numerical experiments under a dynamic condition confirm the efficacy of the proposed method.