Blind-audio-source-separation (BASS) techniques, particularly those with low latency, play an important role in a wide range of real-time systems, e.g., hearing aids, in-car hand-free voice communication, real-time human-machine interaction, etc. Most existing BASS algorithms are deduced to run on batch mode, and therefore large latency is unavoidable. Recently, some online algorithms were developed, which achieve separation on a frame-by-frame basis in the short-time-Fourier-transform (STFT) domain and the latency is significantly reduced as compared to those batch methods. However, the latency with these algorithms may still be too long for many real-time systems to bear. To further reduce latency while achieving good separation performance, we propose in this work to integrate a weighted prediction error (WPE) module into a non-causal sample-truncating-based independent vector analysis (NST-IVA). The resulting algorithm can maintain the algorithmic delay as NST-IVA if the delay with WPE is appropriately controlled while achieving significantly better performance, which is validated by simulations.